That sounds good: no free speech for Nazis. But how about others? We could say no free speech for misogynists; we could sign on to that too. Soon, we will have other categories of people that don't deserve free speech.
But then the next step is for no free speech for an old leftie organization, the ACLU, long attacked by the right for defending Communists and atheists. If the ACLU defends free speech for Nazis, then they should be shouted down too, right? (As they were by BLM protestors at William and Mary.) Soon, then, free speech is only for someone who defends the exactly correct orthodoxy of the moment, including ideas about what speech should be free or not. If you can't even discuss the issue of free speech, then there is no free speech for anyone, really. At the very least you should be able to discuss that.
Then, as a "card-carrying member of the ACLU,"* I am suspect too, and you are too if you defend me, and anyone defending your right to speak, and so on.
*This phrase was used by George Bush's democratic opponent in 1988, Michael Dukakis, and Bush pounced on the ACLU as a far left organization.