Humans are animals capable of reasoning, they are not reasoning animals.
The ability to reason, use rational thought exists in nearly all humans. However this is a later addition to the brain and the larger 'animal brain' of emotion and instinctual drives pretty much governs most people.
The people who dislike _____________(fill in the blank) don't do it because of rational thought, they do it due to emotions that they can not control, and in most cases don't care to control.
Dislike/Hatred of a minority is a dislike/hatred of other. For most of human history this 'Us vs Them' mentality meant survival of the tribe. In a world of limited resources hating those different allowed you to carve your niche a little bit different.
You are not dealing with an opinion, you are dealing with a feeling. An emotion.
As such you cannot win this word in rational conversation, the raging animal part of the brain is going to resort in animal tactics to respond - anger, frustration and illogical 'this is my opinion, you just have to accept it'.
It also caters to the 'I am better than _______________' - this is a basic animal need. Most of the crap going on in the world that does so much harm is the need to be better than. It is seen starkly in high school with Jocks, Goths, Cheerleaders and all of the other subgroups - each feel that they are better than the other and they have 'good reasons' to list. All are flawed, imperfect human beings who are not better than anyone else.
I tilted at this windmill of Gays are Normal with those vehemently opposed to the idea. The majority I had to battle with had a book to back up their claims (The Holy Bible). Even using that book against them lead to the anger/frustration shut down moment of 'This is my interpretation, just deal with it' which is akin to 'this is my opinion - like or or not'.
What ultimately won what few battles I did win was not my words of reason. It was my actions and behaviors and how I lead my own life as an example to others.
For instance my only having been with 8 men willingly (6 attempts at relationships, 2 one night stands) is in contrast to what most people believe about homosexuals --> a new sex partner every single night.
I also don't force 'gay' down anyone's throat. I'm 'straight acting' and don't lisp, snap my fingers and use 'fabulous' in every other sentence. So I do not come off as a gay man forcing people to accept homosexuality.
These little things did far much more to change the course of opinion than my presenting a ton of scientific data.
Gays are following stereotypes which are viewed negatively. Sadly a lot of the media focuses on the negative - rampant spread of STDS, promiscuity, and its nearly always and over the top nelly queen that represents us gays than a 'straight acting' guy in movies and TV shows. Granted this last is now changing and more and more of the gay characters are 'straight acting'. But I fear the damage was already done.
It is those stereotypes of gays that people fear more than what gays do in their own bedrooms. Its the fear of other, which most likely is what caused the extinction of Neanderthal with only 1.5-2% of neanderthal DNA surviving to the 21st century.
This minor DNA in human genes points out that not everyone is prone to hate out and out, in fact some are actually able to love the different, embrace it, have sex with it.....