To be clear, the content on this website is abhorrent and there's no nuance there. It should almost certainly be forcibly removed from the internet as hate speech.
The nuance is here: all this outrage is being used to demand that Cloudflare becomes a moral arbiter of the content they host, which is a slippery slope because if they accede here, there will immediately be another demand, and another, all using this case as their example. There's nothing to suggest that Cloudflare, as a company, has any skill as a moral arbiter so it seems like a bad idea to demand that they become such. Other tech companies, notably Facebook, are terrible and inconsistent moral arbiters but at least only censor their own platforms. Cloudflare is in the position of hosting other people's platforms.
In any case, I believe the outrage should be directed at whatever legal jurisdiction has power here. IIRC this is a New Zealand website, in which case, wouldn't it make more sense to direct this energy towards getting NZ to issue a takedown request to Cloudflare?