In an article entitled The Attitude toward Hinduism Rabbi Eliezer Melamed writes:
Idolatry B’Shituf
In fact, since on one hand, Hinduism believes in a supreme source for all the gods, and on the other hand, in Hindu worship statues are venerated, offerings are made before them, and incense is burned, Hinduism is considered idolatry b’shituf (ed., the combination of belief in G-d with other idolatrous and alien beliefs). For Jews, who received the Torah from Sinai and were specifically commanded to believe in one God, idolatry with b’shituf is forbidden like absolute idolatry, and the idols and all their implements, images, and sacrifices offered before them, are prohibited by Jews to derive benefit from them.
However, for the B’nai Noach (Sons of Noach), according to most halakhic authorities, there is no prohibition against practicing idolatry b’shituf. Therefore, as long as the idol worshiper also directs his worship to the one God above all the gods, he does not violate any prohibition.
We strongly believe that idolatry b’shituf is forbidden both for Jews and Non-Jews. For an explanation read the post Did Rabbi Moshe Isserles Permit Gentiles Who Are Obligated by the Noahide Laws to Believe in the Creator of the Universe in Partnership With Foreign Gods?
Living under strong censorship in the lands of the exile the rabbis often could not spell out their position on other religions in clear ways. Or if they did spell out their positions in clear ways, the printing companies that published their works decided to use vague code words or totally omit the controversial statements about other religions. After a while religious liberals made inferences from censored texts as proof for their liberal outlook.
Regardless of what you hold about the idolatry b’shituf issue, Hindus and many other Gentiles are anyways guilty of the spiritual crime brought up by Rabbi Moshe Feinstein in Igrote Moshe, Y.D. Vol. 2, Siman 7.
As a side point, since Rabbi Feinstein talks about extra-credit mitzvas for Gentiles, in the source mentioned above, scholars are urged to see what the Rambam himself wrote on circumcision for Gentiles as an extra-credit mitzva in
שו”ת הרמב”ם סימן קמח.
Appendix: Rabbi Yisrael Meir Kagan, known by his nickname “The Chafetz Chaim” wrote a number of important books on Halacha. In Likutei Halachot to the Talmud, Sanhedrin page 56b, the Chafetz Chaim seems to accept the strict view that it is forbidden for a Gentile to be an idol worshiper b’shituf.