One solution is to not volunteer the fact that you train, or get into discussions about it unless someone seems sincerely interested. Think of it like stamp-collecting: why would they care? It's not their thing, so why would you expect them to understand it, or why it matters to you? I don't think that hardcore stamp-collectors get upset because 99.999% of the people they encounter don't get stamp-collecting. They don't "have to face these misperceptions all the time", and neither do we, as long as we keep it to ourselves.
This is very true, and I have learned this lesson over the years. Even then, I would still have times when I would question myself as the result of some event or interaction. I'm done with that for a while.