There’s another problem, though. Claiming that Muslims and Christians worship the same God is an expression of Islamic theology, not Christian theology. But why affirm an Islamic teaching? It’s the Qur’an that claims that the God of Islam is the same God in Christianity (Surah 2:139, 29:46). That means you affirm the Qur’an is correct when you claim Muslims and Christians worship the same God. Now, I’m not saying that everything the Qur’an teaches is false. It can certainly make true claims. But affirming it’s correct on this point leads to another problem.
You have to rewrite biblical history. Why? On Islam’s view, there has only been one true religion since the beginning of time: Islam. Adam, Noah, Abraham, Moses, David, and even Jesus are all prophets of Allah according to Islam. True followers of Moses (allegedly Allah’s prophet to the Jews) and true followers of Jesus (allegedly Allah’s prophet to the Christians) believed in and worshipped the God described in Islam. But that’s not biblical history. Jews and Christians never worshipped Islam’s God. You have to believe the Qur’an and its revision of biblical history to believe they did. This leads to yet another problem.
You have to believe the Muslim claim that the Bible has been corrupted. Why? As noted above, Islam claims that the original and true followers of Christ never worshipped Him, but instead worshiped Allah. That, of course, is blatantly contradicted by what the New Testament teaches. Early Christians never worshipped Allah, but did worship Jesus as God. Muslims get around this by claiming the parts of Scripture where Jesus claimed to be God or was worshipped have been corrupted. Therefore, in order to believe Christ’s original followers worshipped Allah, you have to accept the Bible is corrupted, as Muslims claim.
This is a big price to pay. To believe Muslims and Christians worship the same God, you have to accept a component of Islamic theology, believe a qur’anic teaching, accept the Muslim revision of biblical history, and believe their claim that the Bible is corrupt. Is that worth it? I think the answer is no.