I don’t have a problem with the anthropic principle with regard to the multiverse, or with regard to the solar system, for that matter.
We find ourselves on Earth, not on Mars or Venus, because Earth is suitable for life, Mars and Venus not. Does that cause us to suffer the pains of philosophical conundrums? No, because it’s obvious. Life is going to evolve in places where conditions are suitable and not evolve in places where conditions suck.
Same with the multiverse. We find ourselves in a universe that has the “right” combination of physical laws to make for stable stellar chemistries and the right bonding properties of atoms and we don’t find ourself in a universe in which stars are too cold to burn or in which they flame out in mere seconds. What’s so troubling about that? It seems to me no more or less obvious than life evolving on Earth and not on Venus or Mars.
I think some people are troubled by philosophical conundrums just because they’re put off by certain phrases, like “anthropic principle” (a phrase, by the way, that I think is unnecessary to discuss the possibility of a multiverse)... either that or they just want those $50,000 grants.
Sort of like a person who won the jackpot tracing back each and every step that lead him toward buying that winning ticket, and proclaiming each one of them, divinely designed.
IMO, that goes to the heart of what troubles so many people. Not the anthropic principle, per se, which, I agree with you, has always seemed so obvious that it's hardly worth stating, but the suspicion that it is being used to advance a multiverse hypothesis that may be impossible to ever prove or disprove in the usual scientific sense.