It seems to me that homophobia from many right-wing Christians is just arbitrary cherry-picking to suit their own prejudices.
The Old Testament, written down by some guys thousands of years ago in a culture that is not too different from what ISIS looks like today (all that stuff about obliterating all your enemies around you and leaving none that breathe and taking their virgins, killing people with fire or stones that break your rules, and that sort of thing), mentions all sorts of things not to do, including:
-Don't work on the sabbath. If someone so much as gathers sticks on the sabbath, god wants the community to violently kill them with stones.
-Don't be a psychic medium.
-Don't be a man that has sex with another man.
-Don't eat animals in the water without fins or shells (so no clams, lobsters, etc).
-Don't practice magic.
-Don't eat blood. (no rare steaks?)
-Don't eat pork. (no bacon)
-Don't plant more than one kind of seed in a field.
-Don't cut the hair on the sides of the head/beard.
-Don't marry both a mother and a daughter when you are practicing your polygamist (aka traditional) marriage. In fact if someone does that, you gotta burn the entire group with fire. Basically, just make sure all your wives are not closely related and you'll be fine.
-Don't wear any clothes that mix two types of fabric (such as like half of all modern clothes do).
The character of Jesus in the New Testament didn't bother mentioning homosexuality directly, despite the amount of attention the topic from conservative Christian communities and organizations currently. Much of Jesus' focus was on criticizing rich people, hypocrites, self-righteous folk, and telling people to prepare for the world to end in their generation. He did claim that he has not come to abolish the law, but to fulfill it, that all laws are still in effect, and that anyone doesn't follow the laws and who tells others not to follow the laws will be called least in the kingdom of heaven. And yet he also tells people that it's not what they eat that makes them unclean but what they say (setting aside dietary laws?), tells people the sabbath was made for them not the other way around and it's okay to gather food and stuff. Did he tell people they could start mixing shirt fabrics? Did he say it's okay to plant multiple kinds of seeds in a field? Did he share his views on hairstyles? Why are so many Christians doing these things and then utterly freaking out about gay people?
Then this guy Paul, who wasn't even one of the apostles and had various disagreements with apostles, came along and said some things that Christians use in verses against gay marriage, including where he criticized female homosexuality, for example.
The whole thing is a mix of multiple authors from a far less educated era, and a thousand current interpretations on all of that. What to do? What not to do?
And what do people focus on today? Just the gay thing. Not the other things. Even though homosexuality is not any more prevalent in the Bible than most of that other stuff that they ignore. There are protests against gay marriage. Major lobbyist organizations doing major initiatives to keep lgbt rights as limited and unequal as possible. There have been countless threads against gay marriage and other gay rights on this forum.
But where are the Christian protests against stores selling clothes with mixed fabrics? Or people that refuse to sell mixed-fabric clothes to customers because it violates their religiuos beliefs? How many Christians even bother to check their tags to see what their clothes are made of? Where are the people telling barbers they shouldn't be legally allowed to cut the hair on the sides? Why is almost every Christian eating whatever she or he wants, including pork, blood, and shellfish? Why do so many people do all sorts of work on the sabbath when they don't economically need to? Are there large Christian organizations trying to pass laws to ban mediums? If they're not doing most or all of those things, why do they get all activist when it comes to gay marriage?
Homophobia is still a present thing. A lot of people use religion to justify theirs, even when they disregard everything else their religion says.