"Do the classically trained musicians generally tend to be more competitive?

I doubt it. I've seen just as much 'jealousy' and competitiveness in folk groups as I have in classical circles. That always ruins the enjoyment, for me.   A lot of people don't even TRY to develop their musical talents because they think "oh, I'll never be as good as so-and-so, so what's the point?" I think that's really sad, and a true waste of potential.

"Does anyone teach people how to play with love? ... or is it a self-taught thing?"

For some, it just comes naturally. But for everyone, having a teacher or musical 'mentor' who plays with expression and love, who really does LOVE music for it's own sacred sweet sake, is the best "instruction" of all. The students pick it up as if through "osmosis".
Even if they have the dreaded task of learning how to read music as well! Love prevails, even over the written score!!!

:>)    daylia (all full of love now!)