I suspect that there might be a few answers.
Perhaps its a hangover from a previous age where homosexuality was illegal and frowned upon ?
Possibly due to ignorance.
Possibly due to their religious teachings.
Maybe something in their own psyche that drives it.
My own view is quite simplistic. Its none of my business who people want to shag. And it doesnt affect me in any way if two people of the same sex want to get hitched. Good luck to them, we need more love in the world.
I would suggest that my view is a conservative one and is shared by the majority of decent conservatives.
In our lifetime homosexual activity could get you arrested, and it still could in some of the more backward countries of the world. Do you want to see us make common cause with the likes of Saudi Arabia ?
Ok only like one guy I know of actually got aressted for homosexuality. And that wasn't even about him being gay. A jealous lover called in a fake robbery to catch him with another guy and the guy was acting belligerent and the cops wanted to charge him with anything they could find.
Secondly this op is a loaded post. But to answer you're question since you can't seem make the giant leap of trying to understand and empathize yourself. They view marriage as a holy sacrament between them and God, and they don't want to see that turn into a mockery in front of God, so they turned to the government to force their way upon other people. Which is bad...but let's not pretend the other side does not wish to use the government in the same way. People against gay marriage are absolutely entitled to their own beliefs, they shouldn't be using government to get their way.
Thirdly, do you think Hillary is some mighty fortress for gay rights?? After all as a senator she did say that Heterosexual marriage is a fundamental pillar in America and should be protected as much as possible. And yes Saudia Arabia is one of the worst countries when it comes to human rights across almost all spectrums, so why do we keep supporting politicians who butter up to them for their donations?!?!? This includes Hillary, Obama, the Bush's and pretty much 80% of senate and congress.
Lastly, the Supreme Court ruled that gay marriage should be left to the states to decide back in 2012 or whenever that was. They then went against that ruling a mere 2 years later and said states have no say in the matter. There is no other way to look at their rulings and say they are not an activist Supreme Court, why is that bad. Because 9 unelected officials should have no place in acting on what their personal beliefs are. Let's imagine by some miracle October surprise, trump and hackers comes out with some really damning evidence on Clinton and trump wins. Now trump nominates judges who will be more supportive of his fascistic policies...do you really want the people in the Supreme Court to have the type of power to sway us into fascistic rule, much like they gave themselves the power in the most recent gay marriage ruling??