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According to Rambam and Noahide Laws, Christianity idolatrous but not Islam

Prohibition of inventing a new religion for the peoples of the world

Everyone who invents a religion for himself rejects the commandment of the Almighty for all the peoples of the world in the seven commandments and violates the very essence of these commandments.

Source: "The Seven Commandments of Bnei Noah" volume 1, p. 155-157 Free translation: SHOLEM LUGOV 09.08.2017
As you know, the Almighty commanded the seven commandments for the nations of the world (Bnei Noah) and passed them on through Moshe-rabeina. And the Almighty also ordered through Moses to make the whole world accept all the commandments that were given to Noah. And they are not allowed to change the law and come up with additional commandments for themselves at their own discretion... And the one who... invented a new commandment is subjected to corporal punishment and punished in other ways, and inform him that he deserves death for it (from the hand of Heaven); but people do not execute him1.

And everyone who invents a religion for himself rejects the commandment of the Almighty for all the peoples of the world in the seven commandments and violates the very essence of these commandments.

Christian doctrine is idolatry1, as Christians believe that G-d has a material form and through him a woman gave birth to Jesus. There are some among them who believe that Jesus is G-d himself with his father, then it turns out that there are two deities2. And many of them worship statues and crosses and incument in front of them, and this is already real idolatry.

Islam is not idolatry, as its followers believe only in one God3; despite the fact that their Islam is based on a false prophet who created his religion, nevertheless, those who believe in his prophecy are not idolaters. But in any case, it is forbidden to practice a new religion.

As for the fact that they go to Mecca and to the black stone and fall prostrate there, it is forbidden, as they gather near the monument. Also, those who bow down daily violate the prohibition, as they combine with the worship of the Almighty of their prophet.

Buddhism is idolatry, because although Buddha himself did not proclaim himself a deity, his followers believe so. They create statues and worship them.

Notes:
1) RAMBAM, "Laws of Idolatry" 9:4; "Laws of Prohibited Food" 11:7; "Laws of Kings" 11:4.
2) According to RAMBAM, he is a heretic and idolater. And so RAMBAN wrote in his argument that according to Christian teaching, Jesus is a god. And in his comment on the Torah, he wrote ("Dvarim" 16:22): "And it seems to me that the Canaanites were accomplices of idolaters... and in our time Christians behave like this."
3) RAMBAM, "Laws on Prohibited Food" 11:7. "Tour", section "Yore dea" 124 on behalf of RASHBA and gaons.

Source: https://moshiach.ru/bneinoach/laws/13282.html