I don't think there is any set way; gay or straight to show or own some maturity. I noticed that you said that whereas our straight counterparts get married and have children, we may not have those same liberties... but since when does becoming a parent or a spouse show a level of maturity? An idiotic person can do both of those things (and sadly, I know quite a few) and never really be "grown up".
I also kind of disagree with the whole basis of having a stable parent. I know a few people (including myself) that sort of have their parental figures be anything but of a mature nature (my mother wasn't as horrible, but there are certain areas with her that definitely weren't good to follow after) and yet, still turn out to be some of the most mature and stable people of all. I think it comes from how we view the world, how we want the world to view us and the personal steps and experiences we take on our way of life.
Perhaps I'm slightly jaded; I've experienced a few things in my life that sort of forced me to take a much more realistic view of the world: I've been molested more than once (no, this is not a sob story point. I've dealt with this long ago, my friends; so don't worry), used for sex, have had close friends turn their back on me, had closer friends and family members die of some horrible things and quite a few other events that lifted the rose-colored glasses of immaturity from my eyes. But in a small sense, I do love the sillier and less serious side of myself: I love pop music, I love laughing at stupid little jokes and I probably watch way too many things I have no business watching as a 29-year-old man ("America's Next Top Model"... F*CK YES! :rofl
.
I think "growing up" is something we all do differently and there's no right or wrong way to do so. You don't need to be a parent, a spouse, have a "serious" job, etc. to be one and in truth, some people never do. It's all about how you experience and view life that makes us who we are; not what everyone else seems to think we should be or have.