Now, if the constants ever *do* vary, there goes the weak anthropic principle and the need for the "many universes" (which is not the Everett "many worlds" hypothesis, btw). I read an article by the atheist Larry Krause where he admitted to another atheist that the "many universes" idea was attractive mainly because it eliminated the embarrassment of the weak anthropic principle.
The beauty of the “many universes” theory, as I understand it, is that you can’t observe any of the others (absent wormholes or some such unproven business), so if you want to invoke them you pretty much have to just accept them. Or in other words you have to have faith to avoid Faith.