Seen at Animanachronism:

Quite what the negative consequences of being ‘caught’ are is somewhat unclear, but a hint can probably be found in the phrase ‘One is GAR for men and gay for traps’. Being caught supposedly induces some kind of anxiety about one’s sexual orientation.

I think Daniel can let go of the innuendo safely. The repulsiveness of traps has more to do with plain old indignity of being deceived, and there's no need to dig further.

In the Japanese History section of Natural Science museum in Ueno Park there's an exhibit where an empty glass cubicle and an inviting ramp entrap visitors. After looping on the other side, they see that the empty cubicle terminates the progression of Japanese people from the stone age to our times, and the trapees are used to demonstrate a sample of modern species. When they discover the way prank operates, they feel the same indignation as they would after uncovering an anime trap.

More can be said about various configurations, especially with regards to viewers being fully apprized (Mako?) or not (Bart/B.C.); the former can actually be comical with schadenfreude, unless they associate with the entrapped character. But those are details.

UPDATE: Daniel clarifies:

I think I was aiming at the humiliation people outwardly express on imageboards (’Does this make me gay?’), which is presumably mostly pose. Doubtless the ‘indignity of being deceived’ is what is inwardly felt.

I see.

Speaking of FS/N and the corpus, I guess it was too easy to write the strangeness of the concept off as "LOL Japan", since I'm not British and so I only have a vaguest idea who Arthur was. And the main story was pretty powerful by itself, so I didn't dwell on it. Since Saber didn't gender-swap during the summons, her psyche was not in any way damaged by this specific issue.