Presumably it wouldn't affect your estimate of the validity of your psychological characteristics, but it could quite easily affect your estimate of those traits' unicornosity. It seems reasonable for that to affect or even invalidate your unicorn-identity, even if it doesn't affect your model of how your mind works in any quantifiable way.

But what I'd actually expect to find is more complicated than that: if unicorn-identity works like, say, political identity, it carries not only descriptive but normative components. If you conclusively break the mapping between unicorn-identity and actual unicorn behavior out in the wild, you haven't just invalidated a label; you've also wiped out a bunch of social motivations. I'd expect that to be rather upsetting, and I'm not at all sure how to parse out all the ethical implications.