Marines didn't get involved until they were ordered to start worshipping the Emperor as a God, something which most Marines don't want to do. So as long as neither side starts sporting odd tentacles or threatening or shortchanging the Marines, most Marine Chapters would stay out of the fight.
Uh... that's not why they got involved. Also, there's, like, 35 studio-mentioned Chapters that *do* worship the Emperor as a god. I have a list of them, culled from numerous sources, sitting around on these forums somewhere.