The OTO is a fraternal order, not a teaching organ per se. The A.:A.: is a teaching order, not a social organ per se. It is advised, but not forbidden, that students of the A.:A.: don't associate. Comparing notes, so to speak, could muddy the waters. The Ecclesia Gnostica Catholica (E.G.C.), or the Gnostic Catholic Church, is the religious arm of Thelema you speak of. The reading lists vary from order to order and via specific lineage as well.
"If we are to have Beauty and Love, whether in begetting children or works of art, or what not, we must have perfect freedom to act, without fear or shame or any falsity."