Marriage is a government benefit meant to incentivize and/or endorse something we consider socially desirable.
Social conservatives do not see gay marriage as a social good, because they see it as immoral behavior and/or causing undesirable outcomes.
Because of that, they see gay marriage as an imposition because it uses shared government resources/institutions to incentivize/endorse something they think is wrong or undesirable. They see that as expanding government (and...they're not wrong in the technical sense) for an objectionable reason, so they're against it.
I'm not endorsing this view. I vehemently disagree with it, in fact. But it's not that hard to understand.
But using that logic, anything that the majority feels is "wrong" or "undesirable" (when no actual, demonstrable harm is done) is subject to separate government treatment. It's the same logic that allowed illegal interracial marriage, segregation, "separate but equal", Jim Crow, etc. So yes, it is hard for me to understand how a person would endorse that kind of position when historically it has always ended up making the supporters look like foolish bigots.
Again, these are the same people who talk about gun control using the language "Don't like it? Don't get a gun." And yet when they don't like something, banning it is perfectly reasonable?