The trinity is in the Bible. Not the word “trinity”, but our understanding of it comes purely from the Bible. Which is why even most SDAs agree with it. Real presence (part of the doctrine of transubstantiation) and miracles are also biblical. The New World Translation of the Holy Scriptures and the Book of Mormon, Doctrine and Covenants and the Pearl of Great Price aren’t biblical. Just like how the Qur’an isn’t biblical.
Muslim means “one who submits”, so I could identify as a muslim even though I don’t even adhere to Islam- it doesn’t make me Muslim.
Your second paragraph is the main reason.
I am from the UK and a famous example is Bobby Sands MP. Was a member of the PIRA, but was in prison and got elected MP for his constituency. While I do believe the PIRA to be a brutal terrorist organisation, the people who voted him in wanted to show their support - and I agree with their right to do that as much as I vehemently disagree with their choice