A threat, which I saw on Twitter, is that police and like can try to label anyone as part of the group. Since there isn't something they can use to 'verify' if they are members or not. Not that I can find that specific Tweet now.
But the US government can proscribe only foreign organisations as terrorists.
When they've gone after far-right terrorist groups in the past it's as criminal conspiracies, not under anti-terrorism legislation.
We in the UK can ban domestic groups outright -- National Action, Atomwaffen, various Islamist groups, etc -- but the US has to go after them as criminal conspiracies, because of the First Amendment implications.
While Priti Patel could, a couple of months ago, make membership of Atomwaffen a criminal offence simply by using her powers under the Terrorism Act, Trump can't do the same to a US organisation, still less a movement without any formal structure or officers.