Notice that I said "used the words". That was a deliberate locution on my part. What we have to remember is that he is a politician, and he is thinking about his life after the Presidency. Like any skilled politico, he knows what to say and when to say it.
It's commonly forgotten that Obama had to be prodded into concerning himself with LGBT issues. Dick Cheyney voiced his support for same-sex marriage before Obama did. So did more than a few other Republicans--and Joe Biden, Obama's Vice-President.
I still have to question his true commitment to transgender--or lesbian, gay or bisexual--equality when he accepts as much money as he does from financial-services institutions. After all, they have done more to make and keep people poor--and thus vulnerable to bigotry and violence--than any other institutions, let alone people.
In other words, he is a corporate Democrat who is thinking about the boards he will sit on and the six-figure speeches he will make after he leaves office. The banks and other financial institutions that support him employ a lot of gay men--more specifically, the kinds of gay men who hijacked the LGBT equality movement with their single-minded commitment to same-sex marriage at the expense of all other LGBT issues.
To me, he's only slightly more credible than a Secretary of the Interior who sells Federal land to mining companies.