I think that, as the range of replies here demonstrates, diversity always comes at the price of a certain tension; the minute that differences are recognized, there's a judgement that takes place. Here's a classic, and from someone who loudly vaunts his own "socially tolerant/progressive/liberal" POV:
It will always have a stigma as it is an abnormality.
Yes it naturally occurs.
No it doesn't make one a bad person.
But it doesn't lead to the survival of the species.
So for that alone I think it will always be seen by some, if not many, as odd - stigma if you will.
He uses a variation on one of the words I've tried to eliminate from my vocabulary (normal), because it's only meaningful if you believe in a superior "norm", and I do not. His belief that there's a superiority in being "normal" is illustrated again (and even more clearly) by his use of "odd" in his final sentence.
But it also illustrates that he doesn't understand what a stigma is (for that matter, neither does the OP), as it's not the same as a prejudice, for instance. It's not something that simply is, it's
something which is carried by those to whom subjectively it's applied:
Modern American usage of the words "stigma" and "stigmatization" refers to an invisible sign of disapproval which permits "insiders" to draw a line around the "outsiders" in order to demarcate the limits of inclusion in any group. The demarcation permits insiders to know who is "in" and who is "out" and allows the group to maintain its solidarity by demonstrating what happen to those who deviate from accepted norms of conduct (Falk, 2001). Stigmatization is an issue of disempowerment and social injustice (Scheyett, 2005).
There are some stigmas which I recognize and apply, for instance: to drug addicts or child molesters or white supremacists (no, I'm not equating them, merely listing them as three relatively easy targets for stigma application). I stigmatize drug addicts because experience has taught me that I cannot trust them and that, eventually, they will steal from you in order to maintain their addictions. I do not extend this stigma to someone who is no longer using, though I would probably continue to have trust issues with them until proven unjustified. Child molesters/pedophiles can also at least attempt to control their behaviors, though I do not believe that they can be "cured"; I don't pretend to have any answers on how they can be integrated into a larger community. Since white supremacists don't even recognize that their hate is a symptom of pathology, I am even less sympathetic to them than I am to child molesters.
I believe that I am completely justified in applying a stigma to the people I've listed above; there is no place in my life for any of them. And even if no specific criminality can be pinned to a white supremacist, I feel that their views alone justifying my viewing them as a pariah and excluding them from my sphere.
As to the OP: in a word, NO. There are large populations who believe in stigmatizing women for gawd's sake, and womanhood is statistically the largest human majority in the entire world. With that level of stigma still actively perpetrated around the globe, I see no hope for LGBTs. That's why I've always specifically chosen to live in places where my sexual orientation is a non-issue.
I can't change the world, but I can choose which piece of it I inhabit. I don't care what anti-gay bigots think of me any more than I care what drug addicts, child molesters and white supremacists think about me. As long as they're not actively intruding into my journey of life, liberty and the pursuit of happiness I can ignore them; if I feel as though I am being personally targeted, I'd have no problem coming up with ways of creatively neutralizing their threat. I've done it before and will do it again, no doubt.