I actually agree with all of that even if I would have worded it different. But this is essentially just my position restated in a complimentary way.
If person X comes to a game and says, "I'm sorry, but this game can't contain spiders.", as much as he might not want to divulge why, civility requires he have some sort of conversation about it to explain to the group why his request is reasonable. That explanation need only be what you've imagined here, "because I have a phobia." At this point we have a polite request with a valid reason, and now the GM should either grant the request, or if for some reason he can't grant the request, must apologize and try to politely explain why he can't grant the request. This is just basic human civility. It's common sense.
When someone writes a document that tries to overrule basic human civility and common sense, it gets my spidey senses tingling. It suggests an agenda, or it suggests misapplying rules that might make sense in one situation to a very different situation.
Going further into the imagined scenario, doing my duty as a compassionate person requires me to now put myself in the shoes of both the player making the request and the GM, and imagine the situation from their perspective. Or if I'm actually the GM, my duty as a compassionate person requires me putting myself into the shoes of the player making the request and every single other player at the table.
So imagining this scenario, we now have a player that has politely and yet courageously made a request to a group of near strangers. He's probably feeling a certain amount of stress and fear. He doesn't know how I'm going to react to this request. Maybe he's been mocked in the past. Maybe he's afraid that now I know his weakness I'm going to try to use it against him. These are all valid fears. As a GM, I'm going to want to accommodate this request and answer it graciously. Even if the request involves a certain amount of sacrifice on my part, I'm going to want to fulfill it. And in most cases I almost certainly will.
However, again putting myself into the shoes of the GM, the GM has a responsibility to the other players at the table. He's the GM. It's really not fair of him to pass this responsibility off on to the other players. Whether "yes" or "no" he really needs to be the one that bears that burden. Getting buy in on that answer from the other players is also his responsibility. I may well know that there is a player at the table that thinks the request is ridiculous, for whatever reason, and even if they are keeping their mouth politely shut they may want me to say "no". And I have to respect that player as a person just as I respect the one making the request. Additionally, the GM must - if even if only from a practical perspective - enjoy running the game. And there is a point that I can imagine where the sacrifice being asked is just too great, and I must reluctantly and politely refuse to accommodate the request no matter how reasonably it was made.
That intersection of being asked to remove spiders because of a phobia, and NOT being able to accommodate that request on a reasonable basis is likely a vanishingly small edge case. Not only must the player have a phobia, something that really effects only a fraction of the population, but the phobia must be on long tail of the spectrum such that it is is the sort which can be triggered by very weak sensory cues and yet still produce a powerful physiological and emotional response. And this request will have to intersect the vanishingly small percentage of campaigns where the icon, imagery, symbolism, and literal spider is tightly woven into the fabric of the campaign, such as removing spiders from the campaign would effectively mean ending the campaign. I have never run such a campaign, but I know from my preferences in campaigns and my very sincere abiding and deep affection for our eight legged friends, that I am very much the sort of person who might run such a campaign. It sounds really cool. And if I'm running that campaign then I'm going to be very very sad if it turns out one of my friends - or even an enthusiastic stranger - can't be a part of it because of a phobia of spiders.
This is what I think is the common sense, civil, compassionate view of this situation. This is the model I think everyone should have in their head. And therefore, to be quite frank, I'm hostile to any attempt to overturn or replace that model because I think any such attempt will necessarily result in a less civil and compassionate world. And you may reasonably be confused at this point and ask, "How?"
Well, all of the following strike me as possibilities:
a) People will be induced to think that they can make requests without giving explanations.
b) People will be induced to think that they can make demands rather than requests.
c) People will be induced to think that every request they make, even one that is unreasonable, is a reasonable one.
d) People will be induced to think that anyone that denies a request is doing so because they are a jerky unsympathetic uncompassionate person.
e) People will be discouraged from engaging in open and honest and yes difficult conversations.
f) People will be discouraged from being honest and/or welcoming, because they fear that in doing so they are opening themselves up to social censure.
Why do I think none of that is ridiculous fears on my part, and exaggerated concerns?
Because we can see examples of all of that happening in this thread already, particularly from those that think the document is a really great thing.
If a player comes to you and says ‘I’m sorry, the game can’t have spiders,’ civility demands that you respect the player’s boundaries and remove spiders from your game.