Often, but not exclusively. You'd be surprised at the sizeable minority of queer folk who lean right politically and economically, although (luckily for you if your hunch is right) it does seem to be mostly gay men. I've never really understood it. Possibly a combination of internalised homophobia, a sense that they're sticking it to the people who bullied them at school, a desire to pull up the ladder and protect what they've got in a world that isn't always all that keen on them, and a secret admiration for Thatcher's dress sense.
Scratch the surface and it's very often the same people who'd not only gladly jettison the T from LGBT at a moment's notice, but who are sceptical that the B even exists and aren't especially fond of the L. All while flirting with the police at Pride and holidaying in Dubai. Fun!