Asserting the doctrines of a particular religion, or family of religions, requires denying other contrary doctrines?

I think you can hold a sincere interest in different religions and even feel they have wisdom that is worth following and commonalities. You can't though be intellectually consistent and hold a literal belief and be a true adherent of more than one of most major religions. You must acknowledge that you reject and thus disbelieve the claim of divine revelation to certain degrees. Most claim to be the one true and most pure revelation of a god and that it's adherents are to some degree favored. If you were to say you embrace and believe both Christianity and Islam how do you get around Islam doesn't accept Jesus as the son of a god but this is central to being Christian? A Buddhist might not care if you attend a Christian mass but how could you reconcile claiming to accept reincarnation with everlasting life in heaven with the Christian god as embraced by Christians? You might invent some sort of hybrid belief system that tries to marry concepts of both in some way but then you are essentially inventing your own religion. Not that people don't do that all the time but it is not in fact intellectually true to the religions it draws from.

Yeah, as well as rverything else, politics, etc.