we've seen several websites that do not break US law get evicted by registrars, ISPs, DDoS protection services, and other Internet landlords. 4chan miraculously survived multiple mass hysteria periods of the past decade without (iirc) any major disruptions. same as Russian 2ch -- miraculously untouched by Russia's rapid North Koreaization even though its /pol/ is overwhelmingly anti-regime.
Regarding the honeypot allegations, I'm guessing they're referring to the connections between 4chan's founder, Christopher Poole, aka "moot", and Jeffrey Epstein:
There is much farther left than left-libs. The U.S. doesn't get anywhere near as left as it goes. MSNBC is center-left, at most. This is a very right wing country.