Islam purports to worship the same deity as the Jews and Christians. Does this make sense? What evidence is there to support such a claim? If such a statement were untrue, it would unravel the whole of Islam, wouldn't it?
Let us look at the respective natures of Allah and Yahweh.
1. Allah does not enter time and space to communicate with his creation. Yahweh has numerous contacts with his creation, beginning with Adam in the garden continuing through the incarnation in Jesus and culminating in the presence of the Holy Spirit in believers today. This is undeniably a deal breaker in the attempt to argue for identity of Allah and Yahweh.
2. Allah is not constrained by concepts such as logic and reason, he can produce evil, he delights in punishing those who do not believe, yet it is oddly said that he is merciful.
Yahweh is unchanging, always forgiving, always good and always faithful. Yahweh demonstrates love and compassion those who deny him, giving them many opportunities to return to His love.
It was this consistent faithfulness that Abraham relied upon when God told him to sacrifice Isaac...But God had promised to bless Abraham with multitudes of descendants through Isaac. Abraham knew he could rely on God's promise and that somehow God would make this work -- A much different and infinitely more profound story than that of the Abraham written of in the Quran, who submitted to an apparently monstrous command by Allah without any reason to believe Allah would or could make good on his promise. This difference between obedience and submission is food for a lot of conversation.
3. Names: Allah is not a name, but a title, where Yahweh is the personal name of God. If Allah gave the scriptures to the Jews, why isn't Allah mentioned once? Yahweh is mentioned thousands of times in the Bible.
4. Muslims account for the differences between the three faiths by insisting the Bible has been corrupted. On its face, this is a preposterous argument, since the Bible is not just believed to be scrupulously accurate, but historically and verifiably so. Allah's document came through one man, has no documentation even remotely close to the Bible verification.
Interestingly, the Quran says the Bible was not corrupted at the time of Mohammed....so when exactly did this 'corruption' occur? And given the fact that we have early manuscripts of the Bible available from 100 AD, we also have the astounding comparison of Dead Sea scrolls showing the Bible hasn't been 'corrupted' from Jesus time forward.
Try this illustration. If I wrote a book on how to build a chair, and it was translated into several different languages, I might see that in Thai, there was an interpretation of Oak to say Teak or perhaps some Alaska Native translated knife as 'ulu'. Now, there would be discrepancies in the Thai and Alutiq translations for sure, but the message of how to build a chair is still there for both to see.
Similarly, the Bible has been translated from its original Hebrew and Greek into thousands of languages...but the message of God's redeeming and sacrificial love is always there. A much different message than that of mankind's need to submit to a being that delights in death and suffering.