You may be right. However, that makes them, at best, a neutral group. And by her own admission, a neutral group with a switch in her hands. That switch gives her an (additional?) power… and we don’t know whether the other cult members have other powers which could come to bite us in the ass.
One possibility that comes to mind and which would modify our behavior towards them is that they have all the power to search for their fellow cultists and, once they have found them, they gain some additional power to forward their individual win condition.
Unlike the other roles, the third party’s powers and win conditions are unknown. I think it’s in our best interest to get them out of the way. YMMV