Could a Ben-Noach actively practice a religion other than Judaism as long as it isn't considered avoda zara? Suppose, for example, he was born Muslim. Could he continue to actively follow Islam and still be considered to be following the Noachide laws?
While I do not mean to suggest that they cannot have a portion in the world to come, if they do keep the 7 mitzvos, they are nevertheless not permitted to observe another religion:
Yes, a Ben Noach is allowed to practice another religion as long as it doesn't break any of the 7 Noahide laws.
As for your example, according to the Rambam Muslims have no problem with their belief system (obviously there are other issues that the Rambam does have - but that is not within the context of this discussion).
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