It has nothing to do with belief(although I'm sure some militant atheists chose to use lowercase universally, they're likely just grammatically ignorant) . It's noun vs descriptor. Abrahamic God (and Muslim doesn't matter either... it's the same entity in all three) is literally it's name. A proper noun. In your example of Thor, god is just a description, not his proper name. But Thor is not a good example as he's actually a demigod, but demigod is never capitalized as there is no god called "Demigod". Odin is the god of war and the dead... and ruler of valhalla as a more accurate entity to discuss.
God is a god. My god is God. Both of these previous sentences are grammatically correct. The Bible itself even makes these distinctions. Example:
John 10:33-36 (KJV):
33The Jews answered him, saying, For a good work we stone thee not; but for blasphemy; and because that thou, being a man, makest thyself God. 34Jesus answered them, Is it not written in your law, I said, Ye are gods?
Other sources agree.
https://www.learnreligions.com/god-or-god-to-capitalize-or-not-to-capitalize-249823
Other examples of the phenomenon... "The other day, Mom cooked with the other moms." You call your mom "Mom" as a proper noun. Where mom is a general descriptor for the other women your mom was cooking with. "Is she your mom" vs "Mom is calling for you".