"I think there is a 4.3% probability of us getting wiped out by an asteroid"

The mistake here is not the number but the way of saying it: as if this is your guess at the value of a number out there in the world. Better to say

"My subjective probability of an asteroid strike wiping us out is currently 4.3%"

though of course the spurious precision of the ".3" would be more obviously silly in such a context.

Bayesian model requires that probabilities be self-consistent. It breaks Bayesianism to believe that God exist with probability 90% and God doesn't exist with probability 90% at once, or to make confident prediction of second coming of Jesus and then not update probability of Jesus existing once it doesn't take place.

But there is no reason to prefer one prior distribution to another prior distribution and people's priors are in fact all over the probability space. I've heard quite a few times here that Kolmogorov complexity weighting somehow fixes the problem - but the most it can do is leaving different priors within a few billion orders of magnitude away from each other. There is nothing like a single unique "Kolmogorov prior", or even a reasonably compact family of such priors. So why should anyone commit oneself to a prior distribution?

Another argument that fails is that sufficient amount of evidence might possibly cause convergence of some priors - but first our evidence for gray goo or fai is barely existent in any way, and second even infinite amount of evidence will leave far too much up to priors - grue/bleen Bayesians will never agree with green/blue Bayesians.

I have no priors.

You assume a good way of assessing existential risk even exists. How difficult is it to accept that it doesn't? It is irrational to deny existence of unknown unknowns.

It's quite likely that a few more existential risks will get decent estimates the way asteroid impacts did, but there's no reason to expect it to be typical, and it will most likely be serendipitous.