They may earnestly believe in it, but they cannot provide a shred of evidence that it exists and all authority that claims that it does is inevitably found to be either a) mistaken or b) fraudulent.

Very intelligent, otherwise rational people believe in false propositions that make them feel happy, relieved or secure all the time. Unless there's evidence, that belief is as unfounded as the belief of most people that their husband is noble, their wife is beautiful, their child is special, that they deserve what they have, etc. It's a very human, completely fine thing to believe all of these things (even necessary for a healthy life), but when you look at them rationally, you cannot suppose that they are true.

An afterlife doesn't need to be proven false. There just has to be some evidence, (not even proof, just any evidence beyond 'I feel it') to make it a proposition worth considering. Until then, since so many have looked for evidence and failed to find it, the only rational view of the situation is to suppose (and behave) like it doesn't. You're made of meat, death is final, there is no do-over. Make this life count, try to bring about the change that you want to see, because there is no higher authority, there is no second chance.