Yeah, I've heard similar things from Prop 8 supporters. But my personal take is that (for some, at least) the very deeply personal thing they feel, which they feel like someone is trying to take away, is actually antipathy towards people and lifestyles which they haven't in the past had to recognize as legitimate.
I am rabidly liberal, think that marriage between two people—regardless of their gender identity, sexual orientation, etc.—should be legal in all 50 states, and also think that the government should get out of the 'marriage' business altogether. For the foreseeable future, we're stuck with the whole marriage thing for better or worse (hah), so we have to make the best of it.
