This reminds me of a quote my wife often repeats: "Love is not a feeling. Love is an action." It was said in those words by psychiatrist M. Scott Peck in 1978, but you can argue that it also has Biblical roots ( 1st Corinthians, Chapter 13). The idea is that the emotion is all well and good, but it's not sufficient or necessary; with real love, you take care of others, nurture their growth, do things to help them. You can tell that someone loves through the consequences of their actions for other people, no matter what they may say or feel.
I would argue that hate works the same way. Hate is also not a feeling. Hate is also an action. Anger is a feeling, sure. So is the desire for vengeance. So is fear-- of the unknown, of difference, of change. Those are feelings. But hatred is action which results in harm to others.
So when I look at the above-mentioned quote; sure, disagreeing with someone isn't hate. You can disagree with someone perfectly easily. Hate is when you take actions that harm people with whom you disagree, no matter how you feel about those actions-- whether you feel calm, or justified, or even compassionate. Hate is when you vote for someone who makes sure that someone cannot be comforted in illness by the person they love the most. Hate is when you donate money to make sure that children won't have legal protection if one of their parents dies. Hate is when you stand at someone else's parade with signs written to dim their happiness and pride in the thing they're celebrating. All of those are things that do harm, from great to small.
Some right-wing Christians would argue that these actions are done out of love because they're trying to save GLBTQ people from Hell. They would argue that hurting people a little on Earth is justified if it will save them from greater hurt after death-- spare the rod, and all that. That argument... seems very counter to the idea of free will. It suggests that people can't find their own salvation from sin unless that sin is made incredibly difficult to do-- unless the consequences of that sin are financial burdens, physical danger (from untreated illness, from bullying, from murder), social isolation, depression, shame, and guilt. The approach there seems to be "we will save your souls whether you want us to or not." I can see that as a practical means to an end if you think that forced, grudging obedience to God's laws is enough for salvation-- but every Christian I've ever talked to talks about salvation as a conscious, willing process-- a surrender, maybe, but to God, not to humans who beat you into it.
So no, I wouldn't say that increasing the danger to GLBTQ people, increasing our inconvenience and discomfort and financial expense (it cost me $300 at tax time this year to be married to a woman instead of a man. Well-- that's how much extra I paid. I'm not even sure how much more I would have saved in benefits in a heterosexual marriage) can be an act of love. It does us actual harm, physically, emotionally, mentally and spiritually. And the fact that this harm is not new-- that this is harm which has been done for decades, so that it's status quo-- doesn't make us not hurt.
Hate is not a feeling. Hate is an action. It's the action of voting, contributing money, protesting, and speaking in ways that influence others to make my life harder because of who I love. People's feelings don't directly affect me, but their actions do.
That's what we're talking about when we say people opposing same-sex marriage are "hateful."