My other reply to the post about the updateless perspective probably fits better.
I'm not sure what a hypothesis without anthropic reasoning would be. Anthropic reasoning is just that you are certain to observe a world where your existence is possible. if two different hypotheses both allow your existence they both benefit from anthropic reasoning, if any hypothesis ever does. If your existence is drastically more likely conditional on one hypothesis being true than it is conditional on the other being true then the first benefits more from anthropic reasoning itself, while the latter implies more anthropic reasoning for the observation that you exist. Which of those hypotheses would you describe as using anthropic reasoning?
If hypothesis A has a prior of 10^-10, hypothesis B a prior of 10^-15, P(PhilGoetz|A)=10^-20 and P(PhilGoetz|B)=10^-5, then I think it's permissible for PhilGoetz to drastically favor hypothesis B over A whenever the importance of the decision directly scales with P(PhilGoetz).
I believe that life on Earth arose spontaneously. I also believe the galaxy around me is largely devoid of life. I reconcile these things using the anthropic principle.
I also believe that fundamental cosmological constants have values convenient for the development of life. I don't know if it makes sense to pretend that those constants could have had other values - it seems to me like arguing that e could have been 2.716. But it's certainly done. And again, the anthropic principle is sometimes invoked, as an alternative to, say, God.
Suppose somebody came up with a new theory of cosmological constants, that claimed that only certain values are allowable, and that a large percentage of the allowable sets would make life possible. Then you wouldn't have to use the anthropic principle. Wouldn't you be more comfortable with that?
But if that's so, doesn't it mean that you really attach a low prior to the anthropic principle? And that you don't truly accept the anthropic principle?
How do you do Bayesian belief revision when one of your alternative hypotheses uses the anthropic principle? Can you give a strong preference to the hypothesis that does not require it? Because I know that I would.