>When we act to silence white nationalists because we believe their views are false, we undercut our ability to justify our belief that their views are false, by preventing our reasons for believing so from being weighed against their reasons for holding those views, and thus we undermine our justification for the very act of silencing them. And this problem is not unique to the act of silencing white nationalist views. No matter the content of an opinion or the character of its proponent, the act of silencing it is self-undermining.
Please, for the love of all that is holy, consider what white nationalists explicitly want to do. They want to prosecute a culture war, up to and including the marginalization, expulsion, or genocide of left-wingers, non-whites, Jews, Muslims, gays, the mentally ill, and generally anyone not perceived as part of their in-group[0].
I don't even need to go as far as to say free speech is an instrumental goal of something else like anti-racism. Even if you think free speech is itself the final goal, white nationalists are still harmful to you, because censorship is specifically a foundational plank in the platform. This is the sort of thing where the ardent free speech supporter needs to think a few steps ahead and consider what maximizes total freedom at the end of the game rather than the first move.
I'll give you that frequent accusations of being a Nazi are mind-numbing. In fact, Nazis use that to their benefit. But at the same time, free speech supporters should not jump to their defense if those accusations are true.
[0] Notably, what is actually considered the in-group - the "whiteness" to be protected - has no real logic to it; so this list will change all the time based on who swears fealty to whom. American nativists wanted to kill and eat the Irish, Hitler had underlings that wanted to replace Christianity with the old gods, etc.