02/29/2012 at 01:00 PM EST
is comfortable in his own skin.
The actor, whose Oscar date
was girlfriend Stacy Keibler, doesn't "give a s–––" if people think he isn't straight.
"I'm not going to make it seem like being gay is a bad thing," he tells The Advocate
"My private life is private, and I'm very happy in it. Who does it hurt if someone thinks I'm gay? I'll be long dead and there will still be people who say I was gay."
Clooney says his support for marriage equality comes from a belief that it is "the final leg of the civil rights movement," adding that he's been a longtime advocate even before Prop. 8 became controversial in California.
"I've made the point that every time we've stood against equality, we've been on the wrong side of history," he says. "It's the same kind of argument they made when they didn't want blacks to serve in the military, or when they didn't want blacks to marry whites. One day the marriage equality fight will look archaic."
Looking ahead, the actor, 50, says he'd gladly play a gay character if the right opportunity came around.
"I'm certainly not avoiding it," he says. "Whether it's about being gay or it just happens to have a gay character, if it's a great screenplay, let's go do it."