This is an interesting one. It kind of depends on what they play and what genre they play.
If I meet a jazz musician who is self-taught, I probably would expect good things, whereas someone who was "trained" - I'd expect good things, but I'd expect the musician to be different in his or her approach to music - possibly more on the theory and math side of things. (Except for drummers.)
If I meet a gospel or R&B musician who is self-taught, I expect great things, whereas someone who was "trained", I wouldn't necessarily know what to think.
If I meet someone who's into rock, punk, country, metal, etc. and they say they're self-taught, my gut instinct is not a good one - I generally expect loud, obnoxious, and unmusical (in regard to sound, not personality).
This usually doesn't apply to piano players, but it definitely applies to guitarists, bassists, drummers, and DEFINITELY singers.
I generally wait to see whether my initial instinct is correct or incorrect; you can't judge a person until you hear them play. That said, my experiences tend to drive my initial responses when it comes to musicians. I've simply learned to wait to see whether my preconceived notions are valid or not.