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Wiki - The paradox of tolerance states that if a society is tolerant without limit, its ability to be tolerant is eventually ceased or destroyed by the intolerant. Karl Popper described it as the seemingly self-contradictory idea that in order to maintain a tolerant society, the society must retain the right to be intolerant of intolerance.
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.
I was talking about the part:
If Adam is cancelled for being a homophobe, it is within this contract. My question is: Why was Bob cancelled? Has he done or said something? Has he agreed with Adam? Or was there only gossip about his opinion? The reasons for cancelling someone are important. As is causality. Adam and Bob are not functionally identical. Why is Adam a homophobe? Why was Bob cancelled? Maybe the started at the same spot, but here that is not clear.
Another point:
He argues they want to cancel him. How does he know that? What are his arguments, was there a thrat? This reads like an unbacked claim, an accusation. If that's the case, then Bob would be in the wrong for false accusation.
You demonstrate my point.
I set up a scenario with two identical people, differing only in the order in which two independent ideas popped into their head. In every other aspect, they are identical. Any question you decide to ask about Bob, the answer is the same for Adam. Any question about Adam, the answer is the same for Bob.
What you are talking about is valid and important. I readily concede that causality plays an important role in all manner of philosophical discussion.
However, I am trying to get you to understand that these issues are not the only important factors present in this paradox. Indeed, the arguments you presented indicating both Adam and Bob are at fault arises not from the causality chain of intolerance begetting intolerance, but from the context that both are homophobes.
To understand my concern, you need to consider the idea of simultaneity: that both sides sincerely and legitimately believe themselves to have been intolerated by the other, and both sincerely and legitimately believe they are thus justified in canceling the other.
We need to move on to Charlie and David. Both are performing intolerant acts against the other. Both believe the other was the first to act, and both believe themselves to be the victim of the other's intolerance. The paradox has no problem with counter-intolerance. Both believe their own acts justified, and the other's to be unjust.
To David, Charlie's acts of intolerance are fascist. To Charlie, David's acts of intolerance are fascist.
Where the causal chain is disputed (And it is always disputed), Popper's Paradox effectively argues that war is better than peace. I do not subscribe to that philosophy.