It wasn’t just “Nazi rhetoric,” but mainstream political speech that some tried to shove into the box containing the taboo for actual nazism. And if you’re response is to draw “distinctions” then you’re inviting a commensurate response from the other side. We can split hairs and shave down the free speech values until they no longer cover the things we want to be able to suppress. But that erodes the free speech norm. Norms are two-way streets. Both sides have to put up with things they detest and trust that the other side will reciprocate. If there is no trust in reciprocity than neither side has an incentive to uphold the norm.

I would absolutely draw a distinction between government enforced censorship and private platforms censoring content.

Where it becomes a larger problem is if the private platform is an effective monopoly; using monopoly power to censor viewpoints would be a bad. Normally we would call a monopoly platform a common carrier and outlaw censorship by them.