[krapp]

>One side says not using someone's preferred pronouns is intolerant to their gender identity. The other side says being forced to use them is intolerant to their religious beliefs. Now what? Tie goes to the one with the most guns?

Except the paradox of tolerance clearly states that simple disagreement isn't intolerance, nor does it prefer censorship in all cases of disagreement, so your scenario isn't a refutation of it:

    In this formulation, I do not imply, for instance, that we should always suppress
    the utterance of intolerant philosophies; as long as we can counter them by rational
    argument and keep them in check by public opinion, suppression would certainly 
    be most unwise.

What the paradox of tolerance considers to be intolerance, and thus open for censorship, are views which do not allow for rational debate, or respect the existence of opposing viewpoints, but which resort to violent suppression of those viewpoints and the people who hold them:

    But we should claim the right to suppress them if necessary even by force; for it 
    may easily turn out that they are not prepared to meet us on the level of rational 
    argument, but begin by denouncing all argument; they may forbid their followers to
    listen to rational argument, because it is deceptive, and teach them to answer 
    arguments by the use of their fists or pistols. 

That seems like a clear principled line to me.

[AnthonyMouse]

This is a classic motte and bailey. The motte is that "intolerance" only means the denunciation of rational argument and calls to violence. The bailey is that this justifies blocking the entire opposition because they are declared to be violent criminals who have abandoned rational argument, or expanding of the definition of "violence" to mean (warning: irony) any rational debate about sacred cows.

[krapp]

>The bailey is that this justifies blocking the entire opposition because they are declared to be violent criminals who have abandoned rational argument, or expansions of the definition of "violence" to mean (warning: irony) any rational debate about sacred cows.

I never made or implied any such claim, you're not arguing in good faith here.

[AnthonyMouse]

Then your response was a non-sequitur because the context here is that entire platforms are being blocked and the "paradox of tolerance" was put up as a justification.

[krapp]

My response was not a non-sequitur.

You claimed the paradox of tolerance allowed no principled way to draw the line between what should and shouldn't be censored, I quoted the principle as stated verbatim. And rather than make an argument against the paradox of tolerance as written, you decided to switch to ad hominem.

If you want to actually convince anyone of anything, you're going to need to argue against what people actually say and believe, rather than strawmen.