In a word, yes.
For instance, many philosophers (Aquinas, Singer, Pogge, Tasioulas, Shue, just to name some of the better known) think there is a positive duty to supply food to the starving, and also think there is a negative duty not to rob people. Those duties don't have to come into conflict: Aquinas, for instance, said that when a poor person steals from a rich person it is not really robbery because the rich person doesn't really have ownership rights in the thing taken; while Pogge puts forward a model of taxation and property rights in which the needs of the starving can be satisfied without anyone having to be robbed.
You seem to be constructing a hypothetical here for the express purpose of showing why it's not relevant. Presuming that you're attempting to showcase an instance where a positive duty should overcome a negative duty, then I disagree completely.
In regards to the scenario you described, it contains a basic error in that you've inverted a negative duty (e.g. don't let someone starve to death if you can feed them) into a positive duty (e.g. feed the people around you who are hungry), in order to create a conflict.
Now, if you interpret the scenario that way, that's entirely up to you: deontological ethics is not inherently a form of moral absolutism for exactly this reason - people can choose where they rank things on the scale of duties. However, doing so in the manner you described results in having to look elsewhere (as you noted) to resolve the issue you brought up. Far easier, I think, to simply re-order that particular duty.
Similarly, if there were any such duty as you describe it would not colfict with a duty not to suppres, unless I (or someone else) were to enforce that duty by suppressing. Which, to date, no one in this thread has advocated. Exhortation isn't coercion.
Leaving aside the fact that I've said multiple times that personal opinions aren't a moral issue in-and-of themselves, I should point out that you didn't say how - presuming you did find a positive duty to have art showcase empowering images (be it of women or any other group), and a negative duty not to suppress creative expression - could be resolved. This isn't a problem for the one creating the images, since any alterations they make to their own work are part of their creative expression (rather than self-censorship), but someone in charge of distributing that artwork might find it problematic.
I should also note that while no one here (that I've read) is calling for suppression, many people are speaking out against the artwork that they don't like. For the most part, this is pretty clearly meant to be a personal expression of opinion; people are simply stating their tastes. However, when statements are made to the effect of calling something "bad" or "wrong," that sounds much closer to a moral judgment than a statement of personal like or dislike.
As people (understandably) want to see immoral actions curbed, that's something that I find discomforting. Hence why I started speaking out against this in the first place; I wanted to debate (what I saw as the) underlying idea that artwork could be found to be morally "bad."
But in any event, I have not argued for a duty of the sort you describe. No one on this thread is calling for women to be portrayed asexually - the criticism is of women being portrayed as hyper sexualised for the pleasure of the imputed male viewer - and the only duty I have advoctaed is one of not portraying all women as hypersexualised in this particular way without regard to context and content.
The problem here, as I've pointed out previously, is that this strikes me as being full of ambiguities. What constitutes "sexualized" versus "hyper-sexualized"? Does having some women who aren't portrayed that way satisfy that duty as not having portrayed "all" women that way? How does one judge the "context" of a picture (with or without regard to meta-contextual elements)? I find there to be too many personal judgments here to make this a reliable standard.
That is a contentious claim, although not necessarily false for that reason. But you seem to be equating "permissible but not obligatory" with "no moral dimension", and that would be a mistake. Raz and his followers, for instance, think that there are actions which are permissible but not obligatory, but it doesn't follow that they have no moral dimension - part of what makes them permissible is that they realise value, and part of what makes them not obligatory is that there is no obligation on any particular person to realise that particular value.
But even if there are actions with no moral dimension, that does not entail that there are categories of decision - such as deciding what to publish - upon which morality has no bearing. The mainstream view, I think, is that "what I should do all things considered" is intimately connected to "what I should do, morally speaking"; but even those who want to emphasise the distinction beteen these two things nevertheless think that morality is relevant to deciding what I should do, all things considered.
In hindsight, I could have stated my previous assertion better, as I can see how you'd read what I wrote previously and think that I was conflating the two. To clarify, I'm attempting to highlight the nature of actions that are without virtue but that are also without fault (since I think that's an area that is being overlooked), whether because they have no moral dimension whatsoever, or whether because they fall under the category of supererogatory actions.
That said, nothing you mentioned implies that there are not "categories of decision" (a term that I find somewhat too broad) that necessarily have a moral dimension either. It's entirely possible to ask "what should I do, morally speaking?" and find that the answer is "not applicable." At the risk of sounding tautological, morality is relevant except for where it's not relevant.
This is a non-sequitur. Suppose, for instance, that it's superogatory rather than obligatory to try and rescue my neighbour from a blazing hiousefire. It doesn't follow that I can decide whether or not to attempt the rescue without considering any moral dimension. In fact, I have to consider the moral dimension in order to determine that attemting the rescue would be superogatory, and hence that I am permited not to attempt it.
You seem to be running together "relevant considerations" (which moraity always is, at least in the mainstream contemporary view) and "determinative considerations" (which on at least some views morality is not).
See above. I'll admit I should have drawn a clearer distinction; I'm simply trying to point out that there are amoral areas (neither good nor bad), because I perceive those as being rapidly lost in the conversation.
I can fairly easily construct cases where that does matter - eg if you know that, by ordering the chocolate, you will engender the suffering of many people, whereas this won't be so when you order the vanilla, and if nothing else is at stake in choosing a flavour (eg it's not like you have to order the chocolate to stay true to yourself), then it does matter, morally, which you order.
Now let's change the example from one of ordering vanilla or choclocate, to one of ordering steak or salad. In that case Peter Singer has a well-known argument that it certainly does matter. You might disagree with Singer, of course, but you don't show he's wrong simply by asserting that ordering of food is not, per se, a moral matter. Because that claim is precisely what he claims to have refuted.
That's only because you've altered the terms of the hypothetical to the point where it's a different decision altogether that just keeps the same labels. If ordering chocolate means that you've somehow given money to a brutal junta that's keeping the population in their evil chocolate factory (e.g. Willy Wonka, in the original draft

), versus ordering vanilla, which will give money to a hard-working domestic family, then you're not asking "what's the morality of vanilla vs. chocolate?" you're asking "what's the morality of giving money to one of these groups versus another?" and just using "vanilla" and "chocolate" as shorthand.
To put it another way, that's a significant moving of the goalposts.
Likewise, if you are going to contend that choice of what to publish is never morally significant then you have to offer some argument that actualy engaged with those who say that it does make a difference when what you're publishing is (say) hate speech, or some other form of morally or politicaly suspect material.
That is my argument, that such materials don't have the moral characteristics that others imbue them with.
As I said, I don't know any mainstream philosopher who would take that view. From moderns Aristoteleans like Raz and his followers, to Kantians like Onora O'Neill, to consequentialists like Singer, all would think that, before you say or publish something, you should think about its moral value. (Nietzscheans would also agree, I think, that you shuold think about its value, but would contest the idea that this should be moral value. I'm not thinking of them as mainstream, though, at least in English-language philosophy.) Which isn't to say that any of them would advocate suppresion (though some might) - that's a further question. They're talking about the individual's duty as a publisher, not the duty of others to control that person.
This is based on the presumption that I'm advocating that you not consider the moral aspect of an action, which is clearly not my position. I'm pointing out that it's entirely possible to ask that question regarding an action and come back with an answer of "there is no moral aspect to be found with regards to this action." That makes it amoral - much as with a supererogatory-level action where the virtuous thing is not undertaken - and so satisfies that question.
It's also incorrect to phrase the conflict for a publisher in terms of "the duty of others to control that person." Rather, it's the duty of that person not to control the distribution of the free expression of others based on their own personal taste. Even if they feel the work is immoral, it's more important that they let others view it and decide for themselves.
This is mere assertion. What is the argument? I would also say that you make it easy for yourself, with your examples of boats and fruits. I don't want to break board rules, so I won't push the limits, but the claim that (say) the decision to paint a picture of a child in a sexual pose has no moral dimension to it is a slightly harder one to defend, I think. Appeals to intuition won't be enough.
Leaving aside the issue that any argument in regards to moral philosophy is going to come down to personal choice, the argument is that actions have a moral dimension to them (even if that dimension is amorality).
That said, the point of hypotheticals is to make it easy on onesself; their purpose is to demonstrate the point of the person creating them.
Finally, the hypothetical you raised is one that's uncomfortable, but not at all difficult to defend. You may not like such an image, but that's a matter of personal taste, not morality (since ink on paper isn't an actual person, and so should not be judged by that same standard).
My best work in moral philosophy has been published in Philosophy and Public Affairs. I'm pretty well-read in the field, given that I am a tenured academic who teaches and publishes in the area. Rather than telling me I need to study a great deal more, you'd do better at persuading me by actually naming some mainstream moral philosopher who would agree with you that moral considerations have no bearing on decisions about what to publish.
I disagree here. Appeals to authority can be helpful, but they're not the be-all end-all of the discussion. Moral philosophy ultimately comes down to a personal system of beliefs. I believe in the set of deontological ethics that I've outlined here - telling me that they're not in line with Nietzsche, or another well-known philosopher - doesn't undercut the nature of the argument I'm making.
Even Milton Friedman (who is not a philosopher, but who has relevant views nevertheless), who famously said that corporations have no duties other than to pursue profits, was taking it for granted that the government would establish regulations around corporate activity such that the money-making aims of corporations would be aligned with moral requirements. So he didn't regard moral considerations as having no bearing on decisions about production - he was rather arguing for a division of labour, in which government would ensure moral requirements are met by structuring market incentives in the right way.
That's not a division of moral structure, however. Friedman was simply positing that since private enterprises make necessarily-amoral decisions (though I suspect that calling them supererogatory would be more correct), governments need to step in to help promote the general welfare; that doesn't mean that the government is appropriating a moral dimension that's present in those corporate decisions.
I'm not sure what you are referring to by "that", but John Gardner, Professor of Jurisprudence at Oxford University, is a pretty major figure in contemporary deontological moral philosophy. His views aren't quite different from deontological ethics. They are instances of deontological ethics. His view that the criminal law would be illegitimate if it did not track morality is itself a view within deontological ethics. Whereas utilitarians notoriously seem to be commited to a different view of the criminal law, namely that it should not condemn immoral action - ie action that failed to maximally promote welfare (that being the utilitarian criterion of morality) - but rather should condemn or praise in such a way as to maximally promote welfare.
Leaving aside the continued appeal to authority you keep making here, if you want to posit that someone's position backs up your own, please cite an actual source. Saying "this person is an authority, and he agrees with me," isn't enough.
I don't really follow this, but my question to you is: if you think that actions matter morally, how do you individuate them except by reference either to their results (whether internal and therefore necessary, or whether contingent) or to their intended results?
As I've said, morality is determined by the nature of the action itself (e.g. what action
is it?) and then assessing its moral dimension based on the deontological struture. At least, that's how I do it - your value system likely varies.