So had monotheistic Christianity gained an upper hand over Judaism, Islam, Hinduism, Buddhism, etc? How did that happen?
Upper hand? I would say that it just happens that certain Enterprise crew members, the inhabitants of the world seen in "Bread and Circuses" and Dr. Daystrom follow Christianity, which means it still has a strong presence in the 23rd century, but there are believers of other faiths. For example, in TOS' "That Which Survives," Ensign Rahda wears a Bindi (dot) between her eyebrows, which is of religious significance in Hinduism (and other faiths).