Nah, just those who were outright proselytizing and blatantly following a philosophy and or religion that contrasts and or competes with Sith Philosophy and moral teachings. C: AKA - Basic Heresy.
I have a Jal Shey character that is an Ascendancy citizen (not an imperial one) but is frequently operating in Imperial Space do to the Ascendancy being Allies with the Empire. (Hopefully they are still, hard to say post kotet/kotfe since they seemed to be working with the Alliance.) Anyway, he is very much lightside aligned as a force user. So I was wondering if he'd be the sort of person they'd go after. Or if they'd leave it alone due to the conflicts it might bring up with the Sphere Diplomacy and Imperial/Ascendancy alliance. While the Jal Shey study the force from an intellectual perspective with no adherence or belief in the light or dark and religious dogma attached to it, his alignment would read as lightside.