I think you'll find you're far from alone.
Federally, at least, there are actually quite a few in the centre-right who are all for gay marriage. Malcolm Turnbull is the obvious name to drop there, but there are others in the coalition ranks as well, all of them stymied from effecting their views due to their leadership's dismissiveness and unwillingness to allow a conscience vote.
LGBT rights are no longer a far-left issue that they were years ago. They've moved towards the mainstream, to the centre. It used to be just the Greens, then Labor eventually hopped on board, and I expect Liberal will eventually as well. At the moment it's just individuals on the centre-right, but eventually they hit critical mass and things become policy. Most people agree: marriage equality is inevitable. The question then is really why those who oppose it wish to continue building their little sand castle against the rising tide, when all it does is hurt people.
Even on the far right, you still need to look at it at the individual level. Several prominent Republicans in the US support marriage equality despite others frothing at the mouth whenever they hear it mentioned.
I generally think the left/right dichotomy is a flawed system, so I only use it as it helps to illustrate points, but it would pay to remember that people can be very "left" on some issues, and very "right" on others, without being contradictory at all. You shouldn't feel pressure to conform. My understanding is that modern politics is actually more of a four-way system (on an X, Y plane), with progressive and conservative along one axis, and libertarian and authoritarian on the other. It's more a graph than anything else, and people are all over the place, even when they are on the same "side" of politics. And even then, it's only a system that's been developed because humans have this incredible burning desire to categorise things, which don't always need categorising.