Believing in something for which there is no evidence is not deluded, it's just a rather silly way to waste your time and mental energy.
That is why believing in the deist's god, who set the universe in motion but has no further interaction with it, is not deluded but simply pointless. The very reason the notion can't be disproved is because it makes no practical difference whether such a god exists or not. A universe with a deistic god is indistinguishable from one with no god at all; that being the case, the deistic god can neither be proven nor disproven, nor is it useful in any way for explaining why the universe is the way it is.
The deistic god is therefore, scientifically speaking, profoundly irrelevant.
Believing in a proposition which the available evidence, including internal consistency, contradicts is delusion. The god of the Abrahamic faiths falls into this category.
The characteristics normally ascribed to that god, alone - omnipotence, omniscience, omnibenevolence - cannot logically exist together. Omnipotence is self-defeating; an omnipotent being cannot create a force which that same being cannot defeat, i.e. God can't make a rock so heavy even He can't lift it. Omniscience is incompatible with any power at all, because it includes the ability to foresee an action which can then be prevented, meaning the prophecy was invalid. Omnibenevolence, in conjunction with omnipotence and omniscience, is incompatible with the world containing needless suffering; a god which sees the suffering, is able to prevent it and does not do so is obviously not loving in any recognizable sense of the word, unless you are a particularly talented sado-masochist.
I say suffering rather than evil because the doctrine of free will, which is the best answer theodicy has to offer, does not cover agentless suffering. In the specific case of the Abrahamic god, the distinction is largely superfluous, as most of the actions described as taken by the Abrahamic god in the sacred texts can only be described as deeply and directly malevolent. The unprevented agentless sufferings of humanity outside those texts are simply icing on the cake of disproving that notional omnibenevolence.
These are not new observations by any stretch of the imagination; the problem of suffering certainly predates Christianity and Islam, and probably Judaism but the archaeological record gets scarce that far back. Jewish, Christian and Muslim theologians have been struggling to answer the paradoxes for near enough the entire time the faiths have existed, and have not yet been able to do so.
In science, it is perfectly permissible for a theory not to explain everything; at this stage of our development it would be ludicrous to expect anything else. The best and most mature theories will explain an abundance of observable facts, and that is enough to make a theory credible but not useful; to be useful a theory must predict facts before they are demonstrated. A complaint many physicists have about string theory is that while it explains many things it has not yet provided any disprovable predictions. The theory of evolution by natural selection is an example of a theory which is both mature and useful, and not just for enraging creationists either.
What is not permissible is for a theory (or even a hypothesis) to be internally inconsistent or to directly fly in the face of the evidence. The technical term for a hypothesis that does that is false.