When I was an RA in college (public university), we had similar rules... one is, more or less, "on call" 24/7 for emergencies, and my office (next to my dorm room), was considered public space, and I was awakened in the middle of the night a couple times with emergencies. I never thought of leading a prayer meeting, and I guess I would have done that someplace else. Students were only proscribed from using alcohol and other drugs, but otherwise no rules on what went on in their dorm rooms.
Considering the large Jewish population there, "Bible studies" as such never came up ... but neither did "Jewish studies" or any other explicitly religious gathering. There was a yoga class in the downstairs common area. Churches, temples, and even a mosque were within walking distance of campus, so that was probably why..
I don't think being an RA forfeits your constitutional rights.