If they're a force user, they could be eligible, depends on whether there's a good reason to explain why. Not 100% sure, but don't know if there were all that many Force user groupings outside the Sith empire and Jedi order at this time. We don''t know of any offhand, but pretty sure at least a few existed. There were, at this time also several sub-factions to both the Sith and the Jedi, though they were generally defined as part of their order.