People often claim this but there doesn't seem to be any real evidence of it. You get a short-term effect because the target has to regroup, but then they move to a platform with no moderating influences and become even more radicalized. See Voat.
> Secondly, and I think this is the more salient point, encountering racist/sexist/transphobic/whatever speech as a person who is the target of such rhetoric is immediately harmful and othering, especially when these views aren't actively challenged or disavowed by society. This doesn't even include the possibility that hearing hate speech might trigger some prior trauma experienced because of one's identity.
Your theory is directly contrary to various clinical treatments for anxiety (e.g. exposure therapy) which are altogether more healthy and sustainable -- learning to accept that other people disagree with you and have contrary opinions is a much more robust solution than embracing fragility and trying to nerf the world.
Inoculating the population to fascist rhetoric by publicly winning the debate against it with reasoned argument removes its power. Refusing to do so makes it stronger, because then when people are exposed to it, they are more vulnerable having never learned how to defend themselves against it.
> Example: You have a job interview downtown, but you're black and the Klan has a parade scheduled that day, and you're scared of the calls for violence.
You are trying to make a case against speech by making an argument against violence. If the Klan commits violence they should be arrested. If they are deterred from violence by the real threat of arrest then there is no reason to fear going to your job interview no matter what they say.