I always thought it came from "to bind," as in binding a person with vows, in the case of a religious/monastic order, or binding a community together. Etymology Online also mentions the connotation of binding or obliging a follower to a god:Yes, this approach was mentioned in an intro religion course I took way back when. The core idea was "to reconnect" and then the question became "reconnect with what?"
religion | Origin and meaning of religion by Online Etymology Dictionary