The trouble with applying Bayesianism in science is that your conclusion becomes dependent on what priors you think are reasonable. If different people disagree about that, then it becomes a debate about beliefs, not science. (Unless the priors can actually be determined, of course.)

This seems to largely be the case in climate issues, where it's clear that some people have such strong priors against anthropogenic climate change that the evidence needed to convince them outstrip what science reasonably can provide.