The moon does not figure prominently in Judaism. Allah predates Mohamed. What Mohamed did was make the pagan Arabian religion monotheistic. Allah, is Mohammed's tribes name for the moon god, and the Kaaba was built to the moon god long before Islam, which is why the crescent moon is so prominent in Islam.
I hear what your saying and agree with regards to the Islam-Moon connection, as well as the sabre or AK-47, take your pick.
I thought Judaism and the Lunar calendar were related because a 24 hour day in Judaism is not midnight to midnight. The day ends with the sundown, so it is a sundown to sundown system. There is also a marked ocassion of a new month or as it is called Rosh Hodesh - the moon is tied to that, no?