Some people might not want giraffes allowed in movie theaters, that doesn’t mean those people hate giraffes.
Disagreeing with someone isn’t hate.
Disagreeing with someone isn’t hate.
When a gay couple gets married on the other side of the country, do you notice? Does your life change? If it's the mere idea of it you're opposed to, then that's bigotry, not some practical concern like a giraffe blocking your view of the screen.
The word 'marriage' doesn't mean in 2018 what in meant in 1918, or even in 1968, or 1993. In large part, that's a good thing (domestic violence is no longer legal spousal rape is no longer legal, married women don't have a kind of legal-child status), but it's also a bad thing (due to no-fault divorce laws, marriage can be terminated by one party at any time; marriage is no longer the cornerstone of a couple's life, but the capstone to their lives; there's no longer social support for a reliable, lifelong marriage).
Many people who oppose legal recognition of homosexual unions as marriages don't have animus against homosexuals, but rather nostalgia for the previous meanings of marriage. They believe that a stronger concept of marriage makes for a stronger society.
Personally, I think we ought to go all the way and abolish the legal concept of marriage entirely: it's a religious state, not a civil one, and thus not the business of the State. But I understand the concerns of those who worry about how a diverse society which has lost all respect for marriage will survive — I just think we're already there, so we might as well be honest about it.
This urge to thrust "hate" on people is dangerous because is dehumanizes them. If someone is hateful, then they are evil, and evil people deserve punishment.
So the thinking goes, but it is regressive thinking.
The disagreement about gay marriage stems for many from religious doctrine and what is traditional social practice, not hate.
Hatred - a "strong dislike" - does not need to be expressed through fiery emotion. A checklist which says "I will not provide service to someone who is {insert protected class}, followed robotically, is still an expression of hatred.
A computer vision system could be used to implement some sorts of racism, so of course the CV system itself could not be said to "hate" the person. Instead, it's an expression of the hatred embedded in the system.
Someone choosing to follow God's law is expressing the hatred embedded in that belief system. That they might "only" be an instrument of that hatred rather than an instigator does not absolve them.
You wrote "Is it really hate though? Or just people accepting certain social standards and living their lives in accordance."
If those social standard are based in hate, then why shouldn't we say those people are being hateful?
Moreover, if many others from the same society hold different beliefs (e.g., there are Christians for and against gay marriage, and for and against slavery, and for and against tattoos, and for and against women speaking in the church, etc.) then why should we excuse those people who choose a specific interpretation which condones and encourages discrimination?
How many times does the story need to play out? Didn't we just see the #metoo thing play out? These women are victims of hate. Same story with LGBT and black.
No one is dehumanizing anyone. The word is about human autonomy and dignity.