There's the speilwerk or pow-wow folk magic of the Pennsylvania Dutch.
Caste Calvinism? Woah, awesome.
There is nothing in Islam about a moon god. You're grasping at straws.
Explain then the Kaaba.
The presence of a meteorite at an area regarded as a shrine prior to Muhuammad to me suggests that the moon cult idea cannot be dismissed entirely without more evidene than Finn put forth.
In Islamic tradition Abraham built the Kaaba as a monotheistic temple for his son Ishmael, who was the ancestor of all Arabic peoples. Ishmael's decedents later apostatized and brought pagan idols into this temple. So in Islamic tradition the Kaaba was the first temple to the God of Abraham.
In Islamic tradition the Meteorite was a gemstone that fell from God's throne, and has nothing to do with the Moon. The Crescent Moon didn't become associated with Islam until the Ottomans captured the city of Constantinople. You see, the Crescent Moon was the emblem of that city, and the Ottomans used that emblem as their own in an effort to increase their legitimacy.
You're moving goalposts.
Sometimes, I Feel like a Confucian Jew ...Most Abrahamic religions are formally incompatible. You can make them incompatible by jettisoning some parts while retaining others.
For instance, Islamic Christianity could accept the Koran as revelation and Muhammad as a prophet (even, maybe, the last of the prophets) but still accept Christ as the Son of God. A little unwieldy, but possible.
The minor religious movement Messianic Judaism is the sort of thing you have in mind.
Stoic Christianity or Pagan Christianity would be interesting blends. There were some Stoic Christians in OTL and some of CS Lewis' stuff seems to be moving towards a Pagan Christianity, though he never quite pulled the trigger.
I think Confucian Judaism would also be hella interesting, as the kids no longer say.
I've always been really fond of the idea of buddhism melding with European indigenous religions.
Another thing which I've always thought would be interesting would be Christian Plains Indians. I think it would be interesting if they adapted it to their mobile culture. Especially if it were Easterners who did the colonizing or if the Western Liturgy retained the curtain. Nothing would be more lovely than an iconostasis made from buffalo hide!
Allow me to present to you - Apache Jesus...
That one seems particularly weird, because those people are highly religious. And the other high religious colonial settlers in America are famous for, well...