That right there pretty much proves it's not the same god. The God of Abraham never said everyone should be Muslim. The God of the Jews and Christians moved people away from polygamy and made marriage between one man and one woman a sacrament, allah wants them reverted back into polygamists. The God of Abraham made the Jews his chosen people but supposedly allah wants the Jews killed and calls them monkeys. They seem like opposites if anything.
The OT God of Abraham also wanted lots of gentiles killed because, someone said, for their "pagan acts." So the God of Abraham and Allah both share a desire to kill unbelievers. (Not that I believe Abraham, or even Moses, to be historical figures.)