That's not it. It's not a dichotomy. The key to representation isn't "character traits first, minority traits second", it's "character traits first, minority traits as character traits". A character should be a certain way because of who they are, not because of what "their kind" are like.
For example, a lesbian character can be written well by treating her attraction to girls the same way that another character's attraction to boys would be treated. You still get people claiming that her romance-related character traits are just instances of her "being gay" which overshadows all her "real" character traits, but like I said, it's not a dichotomy.