It doesn't seem to me to be possible to hold both rationality and religion in one's head at the same time without compartmentalization, which is one of the things rationality seeks to destroy.

As an example of this class of event, if I were to pray "Oh Lord, give me enough money to never have to work again" and then two hundred thousand people were to buy copies of my books in the next five years, that would be enough evidence that it would be rational for me to believe in God.

The reason why rationality destroys religion is precisely because there is no evidence of this kind. It's not a priori impossible to hold rationality and religion decompartmentalised in one's head, but it is impossible in this universe.