The best solution I found for the Paradox of Tolerance (or, more accurately, for a bigger class of problems that contain that problem) is https://slatestarcodex.com/2018/10/24/nominating-oneself-for-the-short-end-of-a-tradeoff/
The gist of it is that we decide on the following maxim: in conflicts of interest we should favor that cannot easily back off over the side who can.
For example - we want to tolerate a black person existing and we also want to tolerate[^1] a racist person being racist. These two toleration are conflicting. The black person can't stop being black - they were born that way - but the racist person can choose to stop being racist. So we favor the black person's existence, and do not tolerate the racist person's racism.
[^1]: You may argue that we should not tolerate racism at all to begin with, to which I'd say the reason we should not tolerate racism is that there are people who get hurt from it, which is what this maxim is all about.
This maxim is not perfect, of course. It does not apply to all cases, and it does leave up to debate the question of who is forced into the conflict and who is doing it out of choice (e.g. - a conservative may claim that LBGT people are willingly choosing to be so while they are forced, by word of God, to hate them). But I still think it's an improvement:
- It's morally arguable. As long as we don't go into the details, it's easy to defend as a principle.
- The question of who if forced into the conflict and who is willingly entering it can be discussed more objectively than the question of what should be tolerated and what shouldn't (I'm not saying it's always easy to agree - just that the discussion is more objective)
- Even in cases where both sides are forced or cases where both sides are willing, looking at it through the lens of this maxim allows to point at the true perpetrators and/or the true victims, instead of arbitrarily picking one side to blindly side with.