Pumpkin Seeds is sort of right and sort of wrong.
What she's getting into is the dividing line between maximum person rights and societies protection of the rights of minorities. It's arguing that a bigot that hates black people, and only wants them allowed to have demeaning and/or dirty service jobs, has his rights infringed on when he sees black people capable of getting good jobs. He has his rights infringed upon when black people are able to go to college through affirmative action programs, or for some companies to have a hiring preference imposed on them from the government due to affirmative action programs. But that same bigot has his rights imposed on when his taxes go to giving "those people" a free education in elementary through high school. He has his rights imposed on when his taxes help to pay for medical care for "those people", and when his taxes help pay the salaries of police and firemen that serve in "those" neighborhoods.
Now, in a true democracy, where each person only has one vote, and there are no protections in place for people, it's very easy for society to turn into a horrible and evil mob that systematically brutalizes people for being different. Maybe at first, society decides that it doesn't like people who have brown skin, so they're all rounded up and deported. Or maybe they're just killed. Next society decides it doesn't like non-Christians, so all the Jews, Pagans, and atheists are rounded up and likewise done away with. But why stop there? Some people hate gingers. Or stutterers. Or people that drool. Or people with speech impediments. Or people with stupid hairstyles. Do away with them too. And maybe the machine starts turning on itself. It voted to get rid of the non-Christians before. But maybe now it's decided that Mormons and Catholics aren't real Christians, so put them against the wall too.
So, you obviously have to have some sort of protections for people. And at some point, my rights are going to rub against your rights. Society gets the fun job of deciding whose rights supersede the others. If my offense at the smell of ranch dressing knows no bounds and can literally make me vomit, do I have the right to ban ranch dressing? Do I even have the right to ban ranch dressing in my personal vicinity? I don't think so. I think I have to just put up with the disgusting culinary habits of lesser evolved creatures. But what about peanuts? Can I ban peanuts if even the slight exposure to them might kill me because of an allergy? Yes... yes, my life should be protected, even if it inconveniences others to some small degree. So food items should be carefully labeled so I can avoid peanuts, and restaurants should have to go to pains to avoid serving me food that will knock me dead.
Now, between those two extremes, there are a whole slew of rights that people have. It's often the case that these rights come into conflict. So, for some people, it can be very disturbing and impose on their "rights of happiness" to see gay people acting gay. Of course, they're just bigots, but those bigots still have rights. Society's goal has to be to decide if the bigots' "rights to happiness" is more important than gay people's "rights of happiness", which happens to be, in this case, the right to be themselves and act gay in public if they want to.
A pure democracy always just defaults to mob rule, so whoever the majority is gets to make the rules. They could decide to just get rid of all those nasty gay people if they wanted. But in a society like ours, we try to protect the rights of everyone, even from the wishes of the majority. So those gay people can be gay if they want.
So, in the context of this conversation, Pumpkin Seeds is right, in that to allow gay marriage, the rights of bigots to be happy gets ignored. Bigots are being forced to be tolerant. So yeah, she has a point. But on the other hand, fuck bigots.
So, getting back to the topic, does religion have a place in politics? Well, much of the "politics" of religion in this nation revolves around bigotry of one form or another. And, as I so eloquently said before, "fuck bigots." So no, I don't believe that the politics of bigotry should be allowed in politics. On the other hand, religious stuff that doesn't involve bigotry or trampling on someone's rights... well, I suppose I should give a bit on that, and have to tolerate some religious stuff in politics even if I dislike it, because in this case, it's I that could be accused of bigotry for not liking organized religion or (most) Abrahamic faiths, and when it comes down to whose rights are more important, we already have the precedent to "fuck bigots".