My understanding is a US citizen could promote a terrorist organization like Al Queda and that would not be a crime (if no imminent threat) as it’s protected speech.
They could be investigated, but if no crime is committed the won’t be consequences.
If you’re a green card holder you most certainly could have your green card yanked for the same speech.
Green card holders are still immigrants and liable to be removed from the US for a host of reasons that aren’t actual crimes. Heck, “moral turpitude” is a reason for losing your green card, and that includes a whole host of speech that promotes things like war crimes.
Croatia gave him a fair trial and found him not guilty. Despite that he can’t ever come back to the U.S.; this situation is analogous to what the protester from Columbia is facing. Basically, USCIS can decide you lied on an application about a crime they think you committed, without actually being convicted of that crime. (Or in the case of Slobodan Mutic, eventually being found not guilty.)