I think I understood the original post correctly.

I would argue that they can and do frame their arguments in such a way as to qualify themselves as victims of gay/trans intolerance. The most obvious would be any criticism of “cancel culture”. An argument that gay/trans supporters are “canceling” people for minor, not-intolerant slights would justify their counter-intolerance under the paradox, and set up the conditions I outlined.

I would say that your argument is overly technical.

Adam and Bob are both homophobes. Adam argues gay people shouldn’t exist, and then argues that’s gay people want to cancel him. Bob argues that gay people want to cancel him, and then argues that gay people should not exist. With the technical interpretation you have presented, I would have to conclude that Adam has violated the social contract. He has indicated intolerance against gay people first, justifying the counter-intolerance against him. Bob, however, claims to be intolerated by gay people, which then justifies his counter-intolerance of gay people.

I consider Adam and Bob to be functionally identical. I think a valid philosophical model would evaluate them equally. I consider the technicality you describe to be an insignificant error in logic rather than the fundamental operating principle of the paradox.

What you are talking about is more consistent with the “Non-Aggression Principle” than Popper’s Paradox.