"It's not in CloudFlare's philosophy to just take down sites because management doesn't agree with the content,"
...unless the press tells them what their philosophy needs to be? The lesson is that no capitalist company can remain neutral, today. Which has good and bad consequences. It's amazing how the small number of media conglomerates have solidified their political power alongside their commercial power. A true locus of control in Western society.
I learned an important lesson in 2016, my worldviews are not shared in America outside of big cities. It forced me to realize that I didn't even know people disagreed so fiercely because of media conglomerate created echo bubbles.
Many people having non-leftwing ideas simply hide it. Since most workplaces have become politicised and hostile to conservative/right/slightly right of center views, people just hide it. Some people (including me) even engage in fake virtue signalling.
Polling (both opinion polling and actual elections) show that it is very strongly an urban-vs-other thing.
Polling also said that Hillary would win the election, and brexit won't happen. People, including me, lie to pollsters.
I can also sorta understand how the groups in question create a strong(er) emotional reaction. These are hate groups from "our" society. And in the same way that the death of someone close saddens more than a stranger's, seeing a swastika-bearing mob of people who could have gone to school with you may stir more anger than the hate and atrocities committed by strangers–especially if you don't understand their language, and have gotten used to it.
If we interpret Cloudflare's action as a symbol, it may also be more effective when used in this case than with ISIS: coming from (in general terms) the same society, such a signal of disapproval is more meaningful. People are social animals, and they are hardwired to seek approval from their peers. No matter how much someone tries to convince themselves that they don't care, it stings when their neighbour stops inviting them to his parties.
The same isn't true for ISIS, to whom the people at Cloudflare would have always been "the other side".
Plus, obviously, the fact that stormtrooper monthly apparently said that Cloudflare were sympathisers. That statement made it impossible to continue working for them.