Right, obviously it's a problem. There are lots of people who think they've been manifested to, and some of them are schizophrenic, and some of them are not, and it's a whole lot easier to just assume they're all deluded (even if not lying). But even Richard Dawkins has admitted that he could believe in God if he had no other choice. (I have a source if you want.)
Certainly, if you're completely determined not to believe no matter what—if you would refuse God even if He appeared to you himself—then you never will. But if there is absolutely nothing that would convince you, then you're giving it a chance of 0.
Since you are rationalists, you can't have it actually be 0. So what is that 0.0001 that would convince you?
There's a big difference between "no matter what" and "if He appeared to you himself," especially if by the latter you mean appearing to my senses. I mean, the immediate anecdotal evidence of my senses is far from being the most convincing form of evidence in my world; there are many things I'm confident exist without having directly perceived them, and some things I've directly perceived I'm confident don't exist.
For example, a being possessing the powers attributed to YHWH in the Old Testament, or to Jesus in the New Testament, could ...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.