There's an obvious difference between most of the game deities and "real" pantheons, like the Greeks, Egyptian, Norse or Celtic. The focus.
Looking at the standard deities in the DMG or other source books, they are focused on the alignment far more than their main aspects or domains. The domains are almost an afterthought.
Well, I'd say that there are a lot of obvious differences and while the difference you highlight is an important one, I don't think you highlight well exactly why it is important.
One assumption you will find in most game source books is that worshipers worship a deity that has their moral alignment. And that assumption makes absolutely no sense in polytheism. That assumption is actually rooted in familiarity with the Judeo-Christian religion, which has a single god that demands his worshipers behave according to his moral strictures. Rarely do you actually find anything that clear cut in polytheism. Instead, in polytheism worshippers worship the gods for all sorts of reasons and not just sincere devotion and admiration. For example, you might worship a god out of pure propitiation - you don't like the boss but it doesn't make sense to make the boss angry. You might worship a god out of pure self-interest. You might not like the god, but you want success in the area the god controls. You might worship the god communally, and in fact you almost certainly do. This is that god's feast day, so today you are a worshipper of that god just like everyone else. And the thing is, in polytheism you aren't dealing with 'selfish' gods that demand exclusive service, so that's all OK. Indeed, one of the more bizarre aspects of polytheism is service to a deity out of desire to thwart the deity. It's not so much worship as we understand the word, as acts of anti-devotion intended to undermine the gods power. For example, Egyptian polytheism featured big temples to deities of destruction and woe, but not because very many people wanted to see destruction and woe, but rather because there was a priesthood devoted to what we would call prayers (but what they would call spells) of ritually thwarting that deity. So every day the priests of Apep would chant spells of defeat to the statue of Apep to ensure Apep was perpetually defeated. The priests of Apep weren't serving Apep, but his enemy Ra. That's utterly bizarre from the standpoint of how religion is normally treated in D&D source books, which features whole societies strangely devoted to destruction and woe as things 'good' in themselves. But it's far from unusual. For example, in Sparta the principle deities people actually worshipped were Apollo and Athena. They had a temple to Ares, but in that temple Ares the statue (the idol being consider both a symbol of the deity and the deity himself) was bound in chains. Why? Because symbolically this prevented Ares leaving the city and helping their enemies. Consider how weird and unexpected that is if you've been trained with the expectations of most D&D source books, which would undoubtedly portray a city like Sparta as having a war deity as its patron deity and make the cult of that war deity function pretty much like the Catholic Church as reimagined with a Ares as its focus.
Basically, I hate the entire idea of a 'church' in a polytheistic setting, and about the only fault I find with 'The Book of the Righteous' is that it has one. Polytheism doesn't have 'churches'. It has cults (or often, something more like modern fraternal orders such as the elks or the masons) and typical members of society belong to or are initiated into several of them to varying degrees.
The problem with the alignment focus is that in polytheism, you generally don't consider it an immoral act to engage in devotion of some sort to a deity whose morals don't match your own. You don't necessarily compromise your virtue as a LG member of society to engage for a day in the rites of a CN deity of wine imbibing and revelry in and of itself. If you get drunk and transgress against the social order, that's a different matter, and you might not approve of the idea of a day where most people are transgressing against the social order. But the idea of a day where you relax and have a party even in the name of a CN deity in and of itself doesn't offend you. Fundamentally, in polytheism - unlike monotheism - there is no single deity that in and of itself is worthy of exclusive worship, nor does it make much sense for anyone to engage in the exclusive worship of a deity because no deity represents all aspects of human life and is capable of nurturing all those aspects.
This is radically different from monotheism. Yet, we have innumerable D&D source books that nominally describe polytheism and yet assume overtly or by implication that the normal practice of religion with respect to those deities is monotheistic. That is, they describe 'churches' that all seem like variations on Catholicism and bodies of believers that behave as if they had chosen this deity as their monotheistic focus. I think the notion of 'a patron deity' should be actively discouraged, otherwise you get a Sparta that worshippers Ares because of course it does.