I read that about 3% of the population has musical anhedonia, so they don't appreciate music at all. In those cases I'd say it's unlikely classical will change their brains!. I've only ever come across one person who has that condition, Ms Poo's boss. She doesn't dislike music either, it just does nothing for her at all. She often pretends she does like music as she's sick of questions and people feeling sorry for her, although honestly it's difficult not to. First it was disbelief, then I realised she was serious and it was a real condition. To people who can't imagine life without music it's a tough one to process, but I guess if you don't know what you're missing then that's that.
Classical music as understood in common speech is so varied and pervasive that I think many like at least one piece, or a piece of a piece. Maybe that's the foot in the door, but many people get stuck in musical ruts and, as mentioned, it does take some effort to learn to like new things. I've never tried to "convert" anyone, although over the years Ms Poo has gained a taste for it just from hearing me play it. There are genres of music I find baffling, but I would say that's likely ignorance and lack of exposure on my part rather than any inherent defect in them.
I once had an odd conversation with a friend, a fellow classical music fan who thought that EDM was the new classical music. He didn't mean culturally, as in "of the time", he meant literally. Well no, new classical music is the new classical music. My counterpoint was simple though: when we go clubbing we're on a lot of drugs, in fact we're on drugs right now. Let's talk tomorrow.
I bought my mother an early Xmas present - a small music player and a pair of KSC75s. Given her resistance to technology I wanted to make a good impression, so I put Un bel dì vedremo on. She cried for about twenty minutes. Honestly I'm not sure if that's a good sign or a bad sign, they might end up in a drawer either way!