My question to everyone supporting restrictions on speech and supporting privacy violations, even for good reasons, is this: are you prepared to have these tools fall into the wrong hands? The same methods used to quickly shut down a dangerous website or to track down a terrorist by their online posts can be used to silence protests and to hunt down political opposition.
If a different private company wants to host the neonazis, they can go for it. It turns out it's /difficult/ for them because most people find them repulsive.
I don't hear anyone making this argument for child abuse images for what it's worth.