Accepted by whom? I know of no one studying quantum mechanics who invokes or even refers to multiple universes. I’m sure it has a strong following in the popular science press, which all too often plays up the “weirdness” of quantum mechanics to make it seem more exciting and magical, but that doesn’t necessarily correspond to the opinion of the scientific community.
No, actually, quite the opposite. There’s nothing wrong with postulating unusual or unlikely theories, but one shouldn’t expect anyone to take them seriously until they can be supported by experimental evidence. Some theories, such as string theory, are unlikely to ever be experimentally verifiable at any energy or time scales accessible by us and so may never be anything more than elegant mathematical constructs, but at least bring something extra to the table in terms of a more all-encompassing theoretical framework than current models. The fact that people study string theory is not itself evidence of higher spatial dimensions, though.
Of course. But I have no problem assuming that improbable, unprovable things don’t exist.
For example, one could construct a highly unlikely scenario in which a polar bear ends up on the roof of my house while I’m at work. Yet I have no problem stating “I believe my roof to be free of polar bears” on any given day. I’m not asserting I can prove there’s no bear up there at any given instant without physically viewing the roof, but my statement of belief is based on my choosing what I perceive to be the most likely situation given what I know about the world. To do otherwise strikes me as needlessly wishy-washy.