To change someone's mind, the person needs to respect you. Bigotry largely comes from a place of disrespect, so the targets of bigotry cannot change that person's mind.
Now, when my mom was starting down a pretty homophobic path, I had the opportunity to talk to her, to explain that her misconceptions weren't what most gay people were like. Because she respected me more than she respected internet strangers, I was able to change her mind.
But to strangers, no matter how much I type, or how convincing I am, I'm never going to convince someone who's racist or homophobic to stop being that way. They simply do not respect me enough to believe what I say, to trust me over their own friends, family or news sources. I don't have the time to build the trust and rapport with someone to be able to change their mind, so the best thing to do is just minimize the trouble they can cause me by blocking them.