I am single and do have certain "criteria", but I personally don't find it extremely picky. Just stuff like "Don't be a racist", "Be open-minded", "Don't be a jerk", "Don't be extremely jealous/controlling".. .
Superficial things don't much matter to me.
I guess in my case I don't chase closeted people, unless they are willing to come out soon. I would help someone with any sort of coming-out process, but I have no interest in being with someone who has no intention of living openly.