“Islam” is really just the one term for the religion that is most popular. Throughout the ages English has had many other terms for it, including some ending in -ism (definitions from the OED):
- Allahism: “The Islamic conception of the attributes of God; (also) the Islamic religion, Islam.”
- Islamicism: “Islam; (also) the quality of being Islamic in faith, culture, or character.”
- Mohammedanism (and varying spellings thereof)
- Muslimism (and varying spellings thereof)
I’m not sure the reason why all of these went out of fashion. The forms that include Muhammad’s name are considered offensive because they put a mere human above god. “Islamism” and “Islamicism” are now also terms for fundamentalist or militaristic Islam, so it should be obvious why those two terms aren’t more used.
As for Christianity, the religion was originally called “Christendom”. The word “Christianism” was first used in 1576 and is still used as a nonce word when you need an -ism form according to the OED. There’s also “Christism” but that’s much rarer.
Surprisingly the term Judaism was only first attested in a1425 according to the OED. A slightly earlier term for it is “Jewry”.