If they worship the Moon god, they sure don’t worship the same God as we do.
Some people have incorrectly parsed that out from the word "Allah," but actually "Allah" was used for 550 years before Mohammad was born, by Arabic-speaking Christians and for even longer than that by Mizrahi Jews. It simply means "The" "God" --- meaning the Only One.
It ultimately derives from the same root as the Hebrew words "El" and "Elohim", both used in Genesis, and even in a familiar word found in the Psalms, "Alleluia."
The actual Middle Eastern Moon-god, Hubal, is considered a false god of polytheism by Muslims. Osama bin Laden insulted the USA by calling America the "modern Hubal" (meaning "idol.")
The Sura Fussilat (v.37th) shows Islamic intolerance to nature-idols:
"And of His signs are the night and day and the sun and moon. Do not prostrate to the sun or to the moon, but prostrate to Allah, who created them, as it should be Him that you worship."
Look, Islamism is bad enough in itself: we don't have to circulate nonsense that isn't true. It makes us look like fools who don't grasp the advantage of having accurate information.
Think of it -- it was a brilliant plan -- the Jews had the consciousness and unity that comes with worshipping one God rather than a pantheon
The Jews also have the knowledge that they are the chosen people
Mohammed appropriated that (with Ishmael replacing Isaac) completely and also with his victories (and distributing the money and women) built an aura of invincibility
If we say "you are not Abrahamic", they will rush to "prove" otherwise
On the other hand, if we destroy the triumphalism, Islam will crumble