There are lots of erudite and well-reasoned opinions on both sides of the "Is Allah the same as the Judeo-Christian God" question.
No, most would say he is the false god of the moon. Most certainly the Judeo-Christian God in today's world doesn't suggest in any teachings that women should be abused, disfigured and denied human rights as they are under Islam.
This is a cult right there with the UFO Nike sneaker cult! But at least the Nike cult had the good sense to only kill themselves off.