I don't mean this as a condemnation of Obama. After all, he did change his position on gay marriage. However, it's hard not to notice that he opposed it during his first campaign for the Presidency; he finally came out in support of it after Vice-President Biden expressed his.
On the other hand, he did voice his support. Plus, even though he could have been more proactive, he's done more to support transgender people than all of the presidents before him did. Then again, the best of his predecessors did nothing; the others did what they could to make our lives more difficult.
But, as I said, Obama deserves some credit. And, perhaps, he can claim MLK's mantel after all. Nobody knows for sure whether King would have supported LGBT equality, as he was slain more than a year before the Stonewall Rebellion. But we do know that he never said anything negative about queer people, and didn't countenance a "literal" or "fundamentalist" reading of the Bible that interprets Leviticus and other books of the Bible as injunctions against loving people of one's own sex.
Furthermore, King allowed Bayard Rustin, a friend who happened to be openly gay, to serve as one of his closest advisors. Plus, he when he wrote an advice column for Ebony magazine, he responded in a sensitive (though, not surprisingly, pastoral) way to a letter from a boy who confessed his feelings toward other boys. Given the time--1958--it was a very tolerant and forward-thinking response.
Still, some insist that King would not have considered LGBT rights the next logical step in the civil rights movement. One of them is his own daughter, Rev. Bernice King. In 2005, she led a march her father's grave while calling for a Constitutional ban on gay marriage. During a speech at a church meeting in New Zealand, she said her father "did not take a bullet for gay marriage."
But King's widow, Coretta Scott King, vocally supported gay rights. One of her closest aides was gay. (Are you seeing a pattern here?) Furthermore, the FBI tapped his telephone conversations, and he was one of the most surveilled people on the planet. Yet no one could find a conversation, sermon, speech, lecture or letter of his that expressed any sort of anti-gay sentiment.
Given what I've seen and read, I think that if MLK had lived longer, he would have made LGBT equality part of his civil-rights platform. After all, he didn't turn away anyone else whose rights were denied or trampled. I suspect that, being a preacher from the South in the time in which he lived, he simply didn't think much about LGBT people because, well, they hadn't made it onto his radar yet. The same could be said for any number of other people of good will from that time.