The usual pattern is the conquered adopt the religion of the conqueror. That goes back to the sixth century BC when the polytheistic Hebrews adopted the monotheism of the Persian emperor Cyrus.

The Qu'ran explicitly forbids forced conversion. That's why during the middle ages, Jews were safer in Islamic countries than in Christian ones. There are some cases of Muslims ignoring the Qu'ran, just as there are cases of Christians ignoring the Bible, but in general, the story of forced conversion is greatly exaggerated. Start your research here: https://en.wikipedia.org/wiki/Forced_conversion#Islam