If your question was "what makes good theatre," I'd have a hard time answering with non-equity, community theatre, and equity as terms.
However, since you say professional, I have to go to the definition, which has NOTHING to do with membership in a union. I can be a professional teacher, but because I teach at a certain school, I don't belong to a union. To call me not professional is to demean what I do.
In the same way, a non-equity actor isn't somehow "less than" an equity one. In fact, in most productions I see where they cast both equity and non-equity, the non-equity folks tend to be more talented (because they have more people to compete against for fewer slots). It's, of course, not always true, but it often is true.
"Fundamentalism means never having to say 'I'm wrong.'"
-- unknown