Supporting others must be more than condescendingly walking up and saying something like "Hey, you now have *MY* official stamp of approval and it is officially okay for you to be happy with who you are. Even though you are LGBT I'm reaching down to lift you up. *I* want you to be happy." Those were not the OP's exact words, but how I interpret his attempt to reach out. If I am wrong then please forgive me.
The LGBT community, those with autism, mental health issues or any stigmatized segment of our society need for us to treat them just like anyone else with the same level of human decency and kindness we would any other person. No more, no less. We need to do it because we are decent people, not because we feel that we have the right to pass judgement on who they are, or out of some misguided attempt to lift them up because they need our help. That's not respect. I believe respect is shown when you treat others kindly and don't judge or automatically assume them to be lesser and in need of your help to be normal.
I held a door open for a lady one time and the following conversation ensued:
Her: "Thank you."
Me: "My mother taught me to be respectful to a lady."
Her: "My father taught me to never rely on a man and how to take care of myself."
She was right! Somewhere in the back of my head I was treating women like little doves who were fragile and needed to be protected. I told myself I was trying to be respectful, and I still hold doors open for men and women to this day, but I have to be careful that I'm not assuming women are any less capable than men are. It's the same with any other group we want to truly treat as equals.
Equals don't need our stamp of approval. They don't need us to save them. They don't need us to show anything other than the quiet support of treating them with respect and human dignity. If they ask for our help we gladly give it. If they are attacked we speak out and stand with them, but we never treat them as lesser by implying their happiness is something we can grant them.
Again, maybe the OP is sincere, but he needs to understand he is not the savior of the stigmatized. Those groups don't need his approval to be happy, just for him to treat them like any other person with common decency and respect.
And, above all, we need to understand that to truly love others we must learn to love ourselves first.