First, I'm not so sure Harry's claims are as crazy as you're making them out to be. There's at least one charm which violates the second law of thermodynamics, which means some basic assumptions about what's possible and what isn't need to be reworked.

Second, you're comparing the immediate, apparently permanent and total defeat of a Dementor to the warm-fuzzy feelings from religion, and you're also comparing the risk of Harry being wrong about the possibility of eliminating death to the risk of someone with strong religious beliefs neglecting proper medical care. Both comparisons are deeply flawed, due to substitution effects.

If someone wants warm fuzzy feelings, they can get them from something other than religion. A good meal, hanging out with friends, arguing about fanfiction, or even certain types of recreational drug use, provide comparable benefits without the same risks. Other people in the MoRiverse have tried to destroy dementors before, but Harry is apparently the first to succeed, so substitutes simply aren't available. Considering the way partial transmutation works, Harry's attitude toward death may very well be an inextricable part of the technique.

If Harry is wrong, and people will continue to die until the human race goes extinct and all evidence that we ever were slowly fades toward heat-death, if it's really true that nothing can be done about all that, it's not clear (to me at least) how he's making the situation worse by trying. Hastening the collapse by a few minutes, using up resources that might otherwise have produced a slightly more amusing light-show near the end? Insufficient data for a meaningful conclusion, if you ask me. For all we know, his insane obsessions might provide a net benefit to humanity in the long term. If someone is wrong about faith-healing, the consequences are much less ambiguous: sickness and death, which could have been prevented.

Are you saying that there's some way to end death which would, for whatever perverse reason, elude anyone totally determined to find it, but be discoverable by those with a more nuanced attitude? That there's some better, but mutually-exclusive goal? What, exactly, is the black-swan risk you're worried about here?

Killed the dementor the same way he did, except making claims based off a sane model of reality.

It sounds to me like you're just upset that he used the wrong ritual but it worked anyway.