The short answer is YES, Christians and Jews believe in the same God, but NO, "Allah" of Islam is NOT that God. We hear a lot today that "Allah" is just another word for God, but even Muslims themselves say that God is not a "Trinity" and does not have a Son. So by the very words of Muslims, the God of Christianity and Judaism is not the god of Islam.

While the claim today is made by Islam that Allah is the "God of Abraham" and "Creator", a simple review of the historical origins of the religion will reveal this to simply be rhetoric.

Christians and Jews both worship and believe in the One Creator God of the Universe, of the Bible, of Abraham and Moses. However, as a whole, the Jews reject Jesus as the Son of God, and thus, reject the salvation found only in Jesus. So they believe in God, and do worship the True & Living God of whom there is Only One, but they reject Him when they reject His Beloved Son.

(Many Christians believe the Bible teaches there is coming a day in the future when a large number of the Jews will finally turn to Jesus, and become His evangelists in the last days - the 144,000 in Revelation that have turned in faith to God during the Apocalyptic period. Those Christians who believe that the CHURCH has REPLACED Israel - ie. "spiritual Israel" (Replacement or Covenant Theology) - do not believe this more literal interpretation of Revelation and other prophecy.)

After reading the article you referenced...

The article is correct about the Muslims. They worship a non-Biblical, monotheistic deity that was originally one of many common gods of that time and location. The "moon god" was chosen to become a sole deity of Islam by Muhammed, the Muslim founder. (hence the crescent moon symbol of Islam). Muslims do indeed worship "one god" but by Christian, Biblical and even Islamic definition, it is not the same God of the Holy Bible.

Allah was never the God of the Bible, is not a personal god, does not exist in three persons... Allah was NOT, and is NOT, the Creator God of the Universe. Christians should not entertain the idea, nor use it to find "common ground" in religion.

To lump YHWH (Jehovah), God of the Jews and Christians in with Islam's Allah, is a strange and somewhat puzzling answer from a president of a Christian seminary. Many Christian groups, including many Baptists, teach that the CHURCH has replaced Israel, which opens the door for comments and assumptions like this one.  I cannot say if Mohlers answer is based in Replacement doctrine, he doesn't say. I bring the subject up because it is important for Christians to understand this difference, agree or disagree.

The Jews DO worship (or at least believe in) the True and Living God... hence their rejection of Christ is all the more consequential. God has dealt with them severely over post-Cross history because of it.

Many Christians disagree that God still has plans for the Jewish nation, but that doesn't change the answer to this question. The Jews always have, and continue to believe in and worship One Creator God, self-existent, Unique and All Powerful. Yes, they reject Jesus, His Son, and for that they have faced, and will face, judgment.

This "Islam and Jews" comparison, is careless, and in my opinion an inappropriate and misleading answer.  To compare Jews and Muslims as both rejecting Christ would be appropriate. To imply or state that the God of Judaism and Allah are equally false, is not a good comparison and ignores the origins of both.

We must not sugar coat the rejection of Jesus by the Jews, but to compare them with Islam who worship an impersonal, man-imagined, moon god is simply unacceptable from a Bible teacher.

Christians worship God in full by accepting Jesus, His Beloved Son. Jews believe in the same True God as Christians but reject Him by rejecting His Son. Muslims worship Allah, the moon god of Arabia.