Do they say they're on your side but keep raising objections?
Behaviour like this is sometimes called
Opposing something while presenting yourself as one of its supporters, so the objection arrives already shielded from being argued with.
What would tell them apart
A supporter with a real reservation is ultimately answerable — engage with what they're worried about and the objection can actually resolve. What's different here is persistence without resolution: the same worry keeps returning in a new shape no matter how it's addressed, because addressing it was never going to be enough on its own.
Why it might be none of these
Movements and causes contain real disagreement about tactics, timing and priorities, and that disagreement is part of how anything improves. An objection being unwelcome, or arriving at an awkward moment, does not by itself make it insincere.
None of this covers stalking, doxxing, swatting or harassment campaigns. If any of that is closer to what you're facing, go straight to Red lines instead — the advice on this page was not written for it.