At the very least, it seems impossible to say which one should be taken seriously
From the outside, it is. I can't really say someone else's experience isn't valid. If the Buddhist tells me they have experienced Nirvana, I can't reject the veracity of that claim simply because it's presumably incompatible with the dogmatic claims of Roman Catholicism. That makes no sense. No religion can be reduced to a set of truth claims. They all assume that one must practice it, immerse one's self in it, to understand it. I would have to experience the same thing as the Buddhist before I could present a legitimate critique against their experience. Thats the problem.
The problem with the various religions is not their seeming incompatibility to the outside observer. It's the fact that in order to give a legitimate critique of the various religions, one would have to have a lived experience of each one of them, which is not practical since most religions worth their salt assume it takes a whole-life orientation to become suitably immersed to call a religion one's own. Religion escapes legitimate critique precisely because, at its best, it deals in experience. You and I might not get it, but we can't say much about it until we have the experience.
Some vague notion that religions all focus on the idea of oneness or transcendence is so slippery and inexact it would seem to be foundational quicksand
I agree. But, again, if it's true, it's not going to be subject to evaluation by an outside observer. Mystics from various religions will talk about a common element (perennial philosophy, if you will) but you and I can't hand wave it away until we experience the same. I would be interested in hearing from someone who had a mystical experience, say some experience of Nirvana, and said, "Yep, that's complete nonsense. I just had indigestion." Lol
Your comparison with governments seems a false equivalence, as governments are nominally cooperative and administrative entities and by definition flexible and subject to constant modifications and never deal in transcendence or Truth. And don't forget that anarchists would seek to abolish governments precisely because there are no best forms of government
Perhaps it is a false equivalence. I'm thinking a monarch that has absolute power, for instance, is going to be incompatible with a democracy, e.g, the kind Plato deplored. I like your suggestion regarding anarchists, but I think the general idea that a set whose members are incompatible somehow nullifies the veracity of any of the individual members is fallacious, as a principle. All it takes would be one true member, and regardless of the mutual incompatibility of the members in the set, the principle fails.