Well, if we're mistaken in dismissing the evidence theists raise in support of the existence of gods, then of course, with the weight of evidence in favor of it, it's reasonable to assign a non-negligible probability to it.

The important question here is whether the people dismissing the purported evidence in favor are actually correct.

Suppose we're discussing the question of how old the earth is. One camp claims the weight of evidence favors the world being about 4.5 billion years old, another claims the weight of evidence favors it being less than 12,000 years old. Each camp has arguments they raise in favor of this point, and the other camp has reasons for rejecting the other camp's claims.

At least one of these camps must be wrong about the weight of evidence favoring their position. There's nothing wrong with rejecting purported evidence which doesn't support what its advocates claim it supports. Scientists do this amongst each other all the time, picking apart whether the evidence of their experiments really supports the authors' conclusions or not. You have to do that sort of thing effectively to get science done.

As far as I've seen, you haven't yet asked why we reject what you consider to be evidence in favor of an interventionist deity. Why not do that? Either we're right in rejecting it or we're not. You can try to find out which.