I personally don't care whether it's the truth or a lie.
The trouble with religion is that nothing is ever black and white. Everything is always fuzzy. If it's "true," it's never as "true" as the day sky is blue. If it's a "lie," it's never as "false" as the night sky is black. In the good ol' days when we used to have Christianity vs. Islam debates here on these forums, the moon god argument was a favourite. On the Islam side, the idea that Christians were idolaters and polytheists was a favourite. But I always had the feeling that these kinds of discussions were always pointless because of the motivation behind it, which was to put down the other religion and promote your own.
The name "Allah" probably was used to refer to some moon god prior to the advent of Islam and Jews and Muslims are probably right that the Trinity does equate to a form of idolatry, that Christians should revise their theology. But even if this were true, the name "Allah" doesn't refer to a moon god anymore and the Trinity isn't even set-in-stone in Christianity. It's just an interpretation. (Oh, and it doesn't matter what Elohim meant back then. We know the Tanakh is really talking about the God of Abraham, Isaac and Jacob.)
The later Christians got confused about what the early proto-Christians meant with their mysterious terminology. They knew it was important to be "monotheistic." They just forgot what was really "fundamental" and "essential" to Christianity and created a number of creeds associated with the Trinity and Jesus being God. Christianity was supposed to take the Gentile Christians away from pagan idolatry. The Seven Noahide Laws as outlined in Acts 21 was the one "creed" they forgot.
The Quran contains references to important people in the Tanakh, so it has to be talking about the Jewish God Hashem. Who would believe that Abraham, Isaac, Jacob and Moses worshipped a "moon god" named "Allah?" We know it's unlikely they did. The Tanakh wasn't even written in Arabic. It's more likely that "Allah" is equivalent to Hashem.
In religion, you may be able to show how something may be true, but you can never really prove it. That's because what you propose is just a theory. There are other possibilities. To think that your theory is the only correct theory is a very biased attitude.
But bias isn't the problem. The problem is the wrong kind of bias. What would you make of Jesus and his predecessor Hillel saying that loving your neighbour was equivalent to fulfilling the whole Law? That's a pretty biased attitude. It implies that all other commandments are secondary. If you could be kind to your neighbour, all other commandments temporarily become "optional." You'd skip the Sabbath to help your neighbour. After you've finished helping your neighbour, all the commandments become mandatory again.
Nothing is absolute. There are no absolutes in religion. Everything is relative. It's just a question of deciding what's more important. God is important, not because He is absolute, but because of reasons I cannot going into detail here, He's just important. You don't have to believe in God if you don't want to; nobody is forcing you to believe in Him. It's your choice. Do you think God is important?
The moon god argument is silly and pointless because it doesn't really address an important issue. It's a way to put down Islam and that doesn't really help anyone except those who like to play that kind of game. Muslims will simply hit back by saying the Trinity is idolatry or that it assigns partners to God. That kind of game gets us nowhere.
NiceCupOfTea can have his views because as he's told us a number of times already, he had a negative experience of Islam. I'm assuming it has to do with him being exposed to some very legalistic attitudes in Islam, just like there is legalism in Christianity with regards to Trinitarian theology.
Moon god, Trinity or not, Islam will still be Islam and Christianity will still be Christianity.