"Absence of evidence is evidence of absence"

"The invisible and the non-existent look very much alike."

No one can prove that leprechauns, the tooth fairy or that other mythical creatures exist....yet no one in their right mind believes they exist. If anyone believed that leprechauns, fairies or unicorns or whatever, they would be thought to be delusional wouldn't they?

"Religion is regarded by the common people as true, by the wise as false, and by the rulers as useful."

It's impossible to prove that something does not exist (unless you set preconditions, like ice cannot exist above a certain temperature). So until someone can prove the positive, we'll just have to dismiss it and ignore it as a possibility.

That doesn't mean it's not false.

You're definition of delusion is a little thin. According to Google, a delusion is "an erroneous belief that is held in the face of evidence to the contrary." The problem with the (dis-)belief in deities is that there is so little proof either way. That is why it is simply a belief, not a fact.

Saying whether a belief is rational doesn't seem to make a lot of sense. But, as much as humans can be rational, great minds have written rational arguments supporting belief in god(s). And not because these thinkers are in the minority.

Humans are hard-wired to believe in god(s); we are inherently superstitious. In fact, because billions do believe in god(s), disbelief without conclusive evidence to the contrary seems a bit delusional.