At least one .org website that I know of has been shut down because the USA pressured the US organisation that controls the .org domain into doing so.
They could repeat this at will for quite a number of sites.
An immediate step to prevent this possibility, if you run a website, is to register a domain that is controled outside the US.
I have not found one article that just lists them all, and who controls them, but most TLDs have their own wikipedia article, e.g. .org (US controled), .eu (not US controled, yay) etc.
Ultimately ICANN controls all of this, and that's a US orga too, and Trump could bully them into doing shit, too. But the people who know about these things don't seem to think that's a likely threat right now. Also ICANN seems to defer a lot of tasks to exactly these TLD orgas. After all the internet still is (somewhat) decentralized.
We need for Trump et all¹ to make some larger mistakes and do some really stupid things that cause a significant percentage of people to seek alternative ways of access, i.e. enough stupid shit to cause people to set up alternate root DNS systems.
Of course, people with the capacity to do that are like Google et all, who - in that specific example - have set up 8.8.8.8 (etc) and currently seem to be acting pretty decently, but who knows how long that would last, and if a real battle of DNS started up, you'd want stuff hosted by people in other countries anyway, soooo.......
But it seems like we're very far out from that war.