It's getting harder to "run your own website" without the risk of the hosting provider pulling you down if you generate too many complaints and are too much trouble for them.
Remember most hosting providers make a living from customers, and generally don’t pull things down unless it’s super sketchy under their local laws. Dreamhost, Tucows etc. had a reputation for years for being very liberal with their hosting. Pretty much anything goes that’s not blatantly illegal.
And for the many sites with controversy, they probably don’t use a hosting provider.
People used to run entire forums like HN (smaller scale) on their college dorm PC; this is how Slashdot started. It’s not that hard if a college sophomore can do it. As you scale, you probably move to an actual house or building and need more servers and get a leased line from an ISP.
Yes people can appeal to the internet provider(s) but they rarely act. Remember, Stormfront was self hosted for ~25 years and only got torn down because of Charlottesville. Turns out if you actually do things (rather than just talk) with shitty ideas, at least in the USA, this crosses a line.
It's not a slippery slope, it's not harder to run your own website. Don't extrapolate from a few extremist cases.
...and if you are find out what hosting services they use and use one of them.