You are not correct and I can prove it.
If you think the moon and star banner was Islamic, You'd be wrong. Muhammad adopted many local pagan rituals and symbols into his new cult. The moon God was worshipped long before Muhammad showed up. In fact that's where the name "allah" comes from. It's a contraction of "al-ilah `ta ala" which means "The god most high". Contrary to journalistic error, "allah" is not a word for God. it''s the NAME of the Islamic ilah(god) As you can see, and is repeated over 54 times in the Kran, "ilah" is the arabic word for god.
Mohammad at first named his god Ar-Rahman, because the pagan Arabs were currently using the name "allah" for their special black rock and the fragments of it, al-Uzza, Al-Lat and Manat, allah's daughters, literaly chips off the old block.
Muslim have a hard time explaining why pagan Arab said things like "by allah, you are crazy Mohammad", and had names such as Abd-Allah. It wasn't until Mohammad slaughtered his own tribe that he took the name "allah" for his god, never mentioning Ar-Rahman after that. There are some poor attempts by later Islamic scribes trying to cover up these glaring facts written Ishaq.