My religiousness took a hard hit ever since a) I started reading Qur'an and b) kept hearing that Jews, Christians and Muslims worship the same god...
So this is a much more complicated question that each group answers differently.
According to Jews, Christians and Muslims do not worship the same God as them. From a theological / historical perspective Christians are, in effect, a heretical Jewish sect that went crazy and got to big and basically forgot their true roots. Muslims meanwhile are at best a religion founded upon what amounts to religious fanfiction of the Jewish Torah as rewritten by a tribal warlord to provide him religious excuses for his conquest and appetites.
According to Christians, Jews and Christians worship the same God and there is direct continuity from the Jews to the Christians, and that Christianity represents a fulfilling of Judaism and that while Jews are still God's Chosen People, God has extended those blessings and promise of Eternal Life to all Peoples through Christ, which Jews can accept and be a part of too. Muslims meanwhile are at best a religion founded upon what amounts to religious fanfiction of the Bible as rewritten by a tribal warlord to provide him religious excuses for his conquest and appetites*.
According to Muslims, they all worship the same God, but Jews and Christians follow imperfect revelations of that God and that what was revealed to Mohammad is the actually true and perfect version that God wanted told, and the Jews and Christians are, in effect, heretics and fools for clinging to their older revelations and need to be shown the error of their ways... by force if necessary.
From a documentation standpoint, history is more on the side of Jews and Christians in their consideration of Muslims. There's little to no direct continuity between Islam and the other two, unlike there is with Judaism and Christianity. The Quran appears much, MUCH later than any of the other scriptures while many of the stories appearing in it in regards to figures like Abraham, Moses, etc. just appear to be cribbed from the Torah without attestation**. There is likewise no strong continuity of theology in Islam when compared to Judaism and Christianity, which have strong theological ties where one cannot truly understand Christian theology without having some understanding of ancient Jewish religion, as the theology is directly tied.
There are many Christians who consider Islam to be a work of Satan designed to deceive and corrupt God's Word, especially considering how many of Islam's teachings seem to conflict and oppose the theology and morality put forwards in Jewish and Christian scripture while enabling men to indulge in many vices while including just enough moral groundwork to make both a functioning society and also come off not as entirely out of line with those traditions.
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* Note, this isn't the first such religious group to appear like this, there's actually a lot of groups that make these claims of "new revelation" that supersedes the old... Mormons being one of the more famous modern examples.
** Note how this stands in stark contrast to Christianity, which integrates the Jewish scriptures into it's own. Christianity makes no secret of it's links to Judaism nor does it pretend to have more accurate renditions of the Torah than the Jews do. While there is some quibbling over some specific translations between the Torah and the Christian Old Testament, they are much more alike than they are different, and these translation quibbles mainly come from Christians tending to prefer to refer back to the oldest source documents they can find while modern Jews prefer to focus on the Septuagint, a Greek translation of those documents made in the 3rd century BC.