Bigotry isn't the problem in matters of persuasion.
The first is a closed mind, or a strongly defined schema, one built into a person's identity either through hardcoded experiences or through teachings they were never invited to question.
In order to convince an ignorant person to change a core belief, there has to be something that could destabilize those thoughts while not completely breaking them all at once (e.g. realizing everything they knew was a lie and instantly, reflexively rejecting the notion, even if it's, well, conceptually true), to show that the principles they claim to stand for (like basic human decency or goodwill or civil rights) align with something they might have originally thought was counteractive to them.
On the other hand, if someone already knows the same things you do (in terms of being informed) but is primarily motivated by emotional hardheadedness, then you won't be able to fight them with words that they will already expect and anticipate -- the best way to convince them is to present unexpected methods. But this rarely succeeds, and very few people are fitted with the patience and energy to commit to this just to convince one person that maybe they could change what they think at least a little. And the odds are, they probably won't. They are driven by hate, malice, and not just nominally, but genuinely, too; these people are destructive and voluntarily contribute to the problem because they see it as the solution.
Some of these people, a small percent, are immune to change that anyone can methodically engineer. Some people have locked the door and tossed the key.
But at the end of the day, most people, open-minded or not, are definitively changed by one thing, something that's quick and potent and an injection to the veins, and works almost 100% of the time:
Personal experiences.
This is because it provides perspective; it allows a person to change without them having to do anything -- life basically throws it at them and they have to change, because they have new perceptions of something. And because everybody is essentially shaped by the patterns they see in their experiences; and until that pattern is broken, nothing will budge. Conflicting experiences will make room for that paradigm shift, and depending on how severely (and desperately) they cling to their ideologies, they may break down or they may grow.
But that's often beyond the capacity of face to face conversation.
The questions you should ask yourself if you're unsure about educating someone are 1) how much weight will my points/convincing hold, and 2) if that's worth the time, energy, and self-respect I have in my disposal.
The second problem, as other posters have said, is rhetorical ethos. Some people have the power to make others see their way because those people value them. If they can be swayed by knowing someone like them and that they may love/respect is a part of or supports a group of people they were trained to marginalize and think lesser of, they will realize that, 'maybe these two things don't have to be mutually exclusive' and will eventually adapt their perspective around/because of that. This is an issue that comes down to the sort of shortsighted nature of the human psyche, which also irritates me for reasons of its own -- but the truth is that a lot of people are the way they are not just because of their own choices, but because of what they're exposed to. What they can positively relate to. What 'side' they think they should be 'on'. And if you can represent another side while also representing the best of their side, no matter how close or far, then if they aren't too strongly/desperately/indifferently attached they will listen; understand; and eventually, change.