In Islam, I think it is the belief that the Kaaba(not as it is now) was constructed by Abraham and his son Ishmael. They are the ones who kept the black stone in the Kabba.
Though I am myself an atheist, I agree with the OP when he says that idolatry does not necessarily imply polytheism. Anything visual has a more effective impression on our minds. Thus idols/objects are only a means to help visualize in a personal way by associating an image that helps the worshipper concentrate.
I would like to know from the monotheists and anti-idolators, what exactly do they think in their minds when they are praying? I mean, can they describe exactly what goes on in their mind during the process of praying. I don’t believe it is really possible to pray or worship anything without forming some sort of a representative image in the mind. And if worshipping an image makes one an idolator, then by default even though the images may not be physical and is only in the mind, it is an image nonetheless, and so even the monotheists are idolators.
However, it also needs to be said, that cases where Og-like powers start getting attributed to idols and specific places of worship, where praying at a certain location is a better investment than praying at another, where visiting special places of worship is something looked forward to by the worshipper, are those that tend to idolatry. And in that sense, I think all religions have the holier than holy places for their religions.
Robert M. Pirsig’s book Lila has some speculations on the nature of idolatry, among many other topics. He tells the story of how he hooked up with a psychotic woman who was off her meds. (At first, he didn’t know she was psychotic; it took a while before the symptoms showed up.) She found an old baby doll in the trash and started carrying it around, and then started believing it was her real baby, she had somehow given birth to it. When she finally was taken away by those nice young men in their clean white coats, Pirsig realized the doll had become an idol: a physical image into which an unreal meaning had been projected. He set it up in a vacant lot near a dock in New York harbor, giving it a sort of shabby dignity as befits an idol, and then had a conversation with it before sailing away and leaving it there.
Well I think that some of the misunderstanding here has to do with what is really considered Idolatry.
An official definition of Idolatry is as follows:
“Idolatry is a term used by many religions to describe the worship of a false deity, which is an affront to their understanding of divinity”
It goes on to say “However, the term “idolatry” only rarely refers to the worshipping of physical idols”
The reason for this is that christians, jews, and muslims are offended by the worshiping of a FALSE god in general, not simply the praying to some icon of a “false god.” While image-worship or divine honor paid to any created object is going to be offensive to major religions and considered idolatry, this is because it is a FALSE god that is involved. It is not really the simply the icons itself that are the issue at all, but the false god they represent.
None of the big 3 really believe god (or saints) resides in statues/icons, nor do they actually pray to the statues. For those religions that believe that statutes are OK in their faith, the statues are just representations of, as you describe, a formless, or unseen god, and as such are praying to god, not the statute. This is how they distingush between their symbols and idolatry as well- they are praying to their true god.