Does the bigot in you ever experience a pang of remorse?

You are definitely not alone. It is human nature to fear, ridicule or disparage people who ar different from us or what we have known. That said, one can get over it and learn to be tolerant and more caring of our fellow human beings. It starts as you have started with self awareness of the problem and its consequences. Will you ever be 100% free of such prejudices? Probably not. Almost no one really is. But you can work towards it as a goal. You'll find more friends and more understanding if you do, and less tension in your life.