Do Jews, Christians, and Muslims worship the same God?
It’s clear to most people that Christians and Jews worship the same God. The Catechism of the Catholic Church calls the Jewish people “the first to hear the Word of God” and says that, unlike other non-Christian religions, the Jewish faith is “already a response to God’s revelation in the Old Covenant” (CCC 839).
The object of worship for Muslims, however, is unclear for many. The Church dispels such confusion in the Second Vatican Council’s Dogmatic Constitution on the Church Lumen Gentium:
[T]he plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Mohammedans, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind (16; emphasis added).
This is not to say that everything Muslims believe about God is true. But they do believe enough that allows the Church to say that the object of their worship is the same as that for Christians.
For more information on the topic of Christians and Muslims worshipping the same God, see the following articles:
“Allah=God?” by Jimmy Akin
“Christians, Muslims, and the Reference of God” by Edward Feser
“Do Muslims Worship the Same God Catholics Do?” by Tim Staples