Saying the multiverse exists would be more philosophical than mathematical. A judgment of "appropriateness" in math might not be so relevant. Mathematicians are free to explore mathematical options. And scientific models should be testable, or they're not entirely scientific.

The issue here is about self-awareness or integrity. Are we presenting our work as it is or are we pretending we're doing something we're not? If math is a game, we should be up-front about that, rather than pretending math isn't all made up. It's fine to make up models and hypotheses, but they become scientific when they pass certain tests.