Once again, no, multiverse theory was not invoked to explain any variant of the Anthropomorphic Principle. It born out some string theorists trying to explain why gravity is so much weaker than the other fundamental interactions by invoking the notion that the hypothetical gravity-carrying particle, the graviton (which nobody has yet seen, btw) can “leak” into other branes, thus in effect making gravity weaker in our universe. Out of this has grown a set of hypotheses about what these branes are, whether laws of physics can vary between branes, and how branes can interact (ie. two branes colliding might lead to a “Big Bang”).
It’s all hypothetical and I’d wager the bulk of physicists and cosmologists remain unconvinced not only of brane and multiverse theories, but of string theory itself. So let’s get our history straight, multiverse theory does not exist to deny God or anything of the kind. It stems out of a longstanding problem in physics, why is gravity so weak?