The answer is clear to us but not necessarily to non-Christians. Outlawing murder is not imposing our beliefs on others because the vast majority of people believe murder is wrong. The current trend is that the number of people that think gay marriage is wrong is shrinking. Eventually the majority of people will be for allowing it legally. I am all for trying to change public opinion on the matter, but there are Catholic organizations trying to lobby and affect the legislative process to keep the laws in effect.
I’m trying to find strong justification for these actions because to non-Catholics, it looks like we are trying to force our morality onto them.
You cannot say that outlawing murder is not imposing beliefs on others just because most people share that belief. All that means is that you are imposing beliefs on a smaller number of people, but if imposition of beliefs were always wrong, that would also be wrong. The number of people on either side is fairly irrelevant - if imposition of beliefs is always wrong, it’s always wrong.
Some non-Christians (though the argument against homosexual activity does not need to be based on Christian revelation) may disagree about which direction of imposition is better, but that is why we debate and vote and elect people. We do not need to lay down and give up on having moral laws because some people are wrong about morality. (Now obviously, those who disagree would say the same thing to us and think that we are wrong about morality, but all that means is that we must debate and such, not that either side should give up purely because of an idea that we can’t make laws that impose beliefs.)
And again, I say that all law forces morality. That shouldn’t be a problem by itself, otherwise all law would be bad. There are potential problems with such an imposition, namely a) forcing
bad morality or b) forcing morality that should not be forced, but it is not the mere fact that morality is being imposed that makes such things bad.
Those who think we’re wrong could easily argue with us on a). But they can’t argue with us on b), because, of the two positions, theirs is the one that requires more: they would require us to treat a homosexual union as though it is a marriage (even in the purely civil sense as ‘a generally good thing that should be accommodated’) despite the fact that (we think that) it is not, whereas we would simply say that gay people cannot force us to recognize their union as a good thing that should be rewarded with the benefits of civil marriage.
For the most part (although you can find some people who would, I’m sure) we are not advocating telling gay people via the law that they cannot be married, only telling gay people that they cannot force groups who do not think they are married to treat them as though they are.
(There are other arguments against legalizing gay marriage, this is just addressing the ‘imposition of beliefs’ part).