In any case, I rarely unfriend anyone, even people I probably wouldn't have accepted as friends if I had known more about them at the time. Listening to what others think is important. It is especially important to listen to those I disagree with.
I may never change anyone's mind, but if I do, it won't be because I lectured and harangued and imposed my infallible logic on them, Bub-style. I'm all in favor of infallible logic, but have you noticed that people rarely change their minds because of it? Neither will it be because I excluded them from my list of Facebook friends and made them sad. (Oh, the horror!) Changing minds doesn't usually happen by telling people they are wrong. But it never happens when you aren't in some position to communicate with them. Sometimes it happens by listening to people you think are wrong and understanding how they are right. Let them know there may be another solution to the problem that annoys them. Then get on with your own life and don't expect much from them. It's their mind. Ultimately, they have to change it themselves. Or not.