I think you can learn not to react to the stimulus that makes you annoyed. Its a principle of the Alexander technique. You will also notice than Buddhist monks look very calm. I think it would be pretty difficult to get them annoyed.
It's probably the same as with learning about your cognitive biases: First you start noticing your bias right after you did it, then you start catching yourself in the act, and eventually you're able to stop yourself before even doing it.
