As someone of color (Indian) who is often mistaken as being foreign/religious until they hear my accent...

I feel the other commenters here are missing the mark. This isn't about fixing them, or learning to "accept them as they are": bigots should never be tolerated.

Which is to say, your reasons for being "bigoted" towards the bigots isn't a matter of prejudice: you've extrapolated a pattern.

But you don't want to apply this pattern unfairly to people you haven't met, because that'd make you bigoted as well.

Well, I have good news for you: you aren't at any risk for that. Real bigots don't think they're bigots. People with prejudices don't consider their judgement unsound. They think they're the most unbiased, reasonable people in the world, and often try to push their opinions on others with violence, whether it's verbal, social, or physical.

By simply acknowledging internally that you have thoughts that you consider unideal, and unfair, you've done a thousand times more self-reflecting, and have more capacity for self-correcting, than someone like my parents would.

Don't try to beat the bad thoughts out of yourself. Acknowledge them, and pledge to act better than they'd have you.