Woah. So, on this last paragraph I excerpted. There a lot of ... not very neutral language, and I don't really agree with it.
Since the phrase "reasonable accommodations" has come up, I will use that, with an emphasis on the first word- reasonable.
As a DM, if someone told me that they had an issue with something .... let's use spiders, since that is your example ... I would certainly see if I could accommodate their concern. Let's take two scenarios-
A. A player's spouse/sibling was killed by a spiderbite a few months ago. The player says, "Hey, I'm not feeling spiders right now." I would definitely remove spiders from the campaign for a while. That seems like a reasonable accommodation.
B. I advertise that I am doing a one-shot Q1 Queen of the Demonweb Pits. Six people show up, we make introductions, get everything ready, and as we start, one person says, "Hey. By the way, I don't want anything involving spiders." Well, at that point, I'd probably have to continue the adventure with 5 people. There is no reasonable accommodation.
There is an essential element of empathy that I can't find in your post; the idea that a person believes that a weakness is a "trump card" and is trying to ruin your enjoyment. I haven't found that. The whole Rawl's Veil of Ignorance, man. That could be, and, in other contexts, might be me. People just want to game and have fun, and if I can help them by making some de minimis change like "no spiders," that's cool by me.
Just my opinion.