The origins of the myth of Allah the Moon-God stem from the works of a few modern Christian writers (more accurately propagandists) and have widely been debunked.
Oh, that's where it's from. I must admit I was stunned when she mentioned a moon god. I know my Semitic pantheon fairly well, but couldn't remember a "moon god".
I figured that perhaps moon gods have never been very important and are therefore usually unknown (and not worshipped as supreme deity as KFC would have it). I decided to test that hypothesis and asked my (Hindu) flat mate if he knew a Hindu moon god. He said no, but the sun god is important. (He later found a Hindu moon god in Wikipedia.)
It seems unlikely that moon gods make it into the first league of gods. The moon is just something that people don't worship that much, probably because it has to do with the night and most religious people do not think of themselves of creatures of the night (although Christians might think of Muslims that way, but what Paul says about Peter says more about Paul than about Peter).
A more telling quote is directly from the Quran 41:37 which states "ADORE NOT THE SUN AND THE MOON BUT ADORE ALLAH WHO CREATED THEM if it is Him ye wish to serve."
The Quran is the last place KFC would use to learn about Islam.

After all, there are so many people who just make up very convenient lies about Islam, which are much easier to swallow. And KFC doesn't have a problem with that, because the Christian principle of honesty does apparently not apply to statements about Islam.

I am going to guess that you [KFC] have never read the Quran, perhaps never been inside a Mosque.
Well, I must admit I have never been inside a mosque either. I wanted to go to a mosque in Haifa with fellow students (Arab such), but they usually went home for the weekend and there was thus never an opportunity on Friday.
But I did read the Quran (an English "interpretation") and I did learn SOME little Arabic to understand it better.
So no, KFC, I am not kidding. I am just a lot smarter than some and more honest than others. The lot who told you about the Allah moon god theory are either dumb or dishonest. I doubt they were Muslims.
I am secure enough in my faith. I can study other faiths and I don't need people to tell me lies about other faiths to keep me in mine!
And I don't make statements about other faiths without first learning about them (which is why you rarely find me make statements about Hinduism, for example; I just don't know enough about Hinduism).
I have read the Quran, the Tanakh, the Christian Bible (King James and the original German Luther translation), and, just to make it a little bit interesting, I was (luckily) forced to learn Roman and Greek legends in school (I was on a Latin school) and can therefore see where modern western Christianity gets many of its most Christian principles from (Greek legends... ha!).
Now I learn about Christianity from KFC. It's not the Christianity I have known before, admittedly, but it's fascinating.
For example, I have learned that a god associated with a crescent is a "moon god". And I just happened to know, from Greek and Roman history, that the crescent was the symbol of Byzantium, the capital of the (Christian) Eastern Roman Empire. Hence, according to KFC, the Christian god is a "moon god".
And I have learned about the Christian principle of honesty, which apparently allows making up things about the G-d of Islam whenever necessary or convenient. Plus one is allowed to use those lies in a condescending way. There is no need to repent.
Interesting Christianity, I have learned about here.
Since KFC doesn't know anything about Islam (while I do), I will ignore what she says about it.
And I think I should also ignore what she says about Christianity, for obvious reasons.
A "Christian" who believes that Abraham (Abraham!) would teach his oldest son to worship the moon... Unbelievable!