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.
I addressed this issue in my post; I don't disagree, but people who know far more about this than I do not seem to see this as an immediate threat. See the autistici/inventati press release and some comments undermyposts, e.g. from people at OpenNIC. ICANN seems to defer responsibilities, so they cannot - afaiu - pick and choose to block sites as per The Don's will.
If that was a realistic option I think we'd have seen far more shutdowns already.
Of course, ultimately all of DNS is controled by ICANN, a US orga. Trump could effectively shut down the whole internet, we'd have to revert to numerical IPs. A scary thought.