In my estimation, all you need to do to determine if the God of the Bible is the same as the Allah of the Koran is to ask Muslims one question: what is the name of Allah’s Son? Every Muslim will tell you that Allah has no son. The Bible tells us that whoever denies the Son denies the Father, so Allah can not be the same as the God of the Bible.
I don’t know if that means Rick Warren has “renounced” Christianity, but he would at least seem to be badly mistaken on the facts here. He’s not alone, though, there are quite a few denominations of “Christianity” that make the same mistake.
Actually the god they call Allah can be traced back to the Babylonian god Baal.