that's not really true. you're trying to rationalize something by giving it an intellectual veneer. The people who hate us arent scholars and intellectuals worried about lineage or western civilization. She's asking about the very essence of homophobia which elicits great disgust and hatred.

We're hated for breaking gender norms. Gender is about power relations and what you expect from other people, your responsibilities towards them and how you're supposed to treat them. Gender is about what you're entitled to in certain roles. Gay people can elicit massive disgust when straight people assume it means we expect something from them when we dont follow their gender roles and slip into ones theyre not used to. Of course all these things are in the heads of the heterosexuals but they assume certain things about gays and lesbians which infuriate them.

Straight men have certain responsibilities that are infused into their character if they ever want to be a "man". To protect women, to die for them, to sacrifice themselves as "men" when letting the women and children go first on the titanic and be well spoken of or punished and humiliated as cowards if they dont fulfill their duties.

Can you imagine the amount of rage they'd feel if they they felt gay men who were the "bottoms" or whatever but were still males, put a princess tiara on and demanded to cut in line in the titanic above all the men because now these straight men were supposed to be responsible for these gay men they have absolutely no sexual attraction to or duty towards. And the resentment and anger of the women there and their rage at a gay man "stealing their resources", which is the duty of men to "protect" women that women like to exploit and fight and compete over amongst each other. Of course these are all assumptions but they assume if you get fucked like a woman would, then you must want to be assuming the gender role, entitlement and traits of a straight woman, which is where all their assumptions come from

Gender also can become very toxic and can rub people the wrong way. Like how a narcissistic woman can go into a room and expect that every guy wants to do something for her, which just rubs straight men the wrong way. Can you imagine the anger a straight man would feel if some gay person walked into a room and started acting in such a way where he thinks he's some sexy irresistible bimbo and acts like a snotty entitled brat because he thinks he's "cute"?

Straight men and women have also laid claim to certain traits and characteristics for their sex in a competition against one another which sometimes doesnt cut a clean line down the middle because gays and lesbians are down the middle of that line. So women would be highly disgusted and resentful towards gay men because they believe certain human traits are theirs and "how dare gays step into our territory" from things such as empathy, compassion etc and the same goes for lesbians vs straight men.

All of these scenarios are just millions of assumptions made about what you anticipate gay men to be like and what you think they expect from you because of the way they act. Of course it can be reversed, where gay "top" men are seen as intimidating and the rage straight men would feel about being made into "women" and degraded, dominated and debased by engaging in power dynamics with these men who could sexually dominate them.

Heterosexual men and heterosexual women have a great disgust for each other not because of their sex but because of their gender roles. And that disgust they have for each other leaks on to gays and lesbians. Sometimes it's hatred and sometimes its just laughter and mockery. Women in positions of power would be seen as a joke not so long ago. There are some men who would have died of laughter at the thought of a female president because of the assumptions they make about someone's gender (not sex).

All the other answers seem to try and rationalize and give political/structural answers but "ideas" and political beliefs dont inspire disgust towards gays and lesbians. Christian priests didnt just randomly say one day: "ok. you know your gay family members that you have no hatred for? Well, we need to breed more so i need you to uncontrollably be disgusted by them". That's not how any of this works.

Gays and lesbians keep forgetting we were seen as gender abominations in the imaginations of heteros: Gay males painted as cowards by women for not wanting to "serve" them or be manipulated by them because they weren't "man enough" to want the honour of serving a woman and fulfill his role as a man and lesbians were slandered as degenerate beasts who werent interested in pursuing femininity and being a delicate flower to be possessed by a man.

Our entire gay civil rights movement was only allowed to progress when we taught people your sex doesnt have to define your gender and on top of that, gender roles dont always have to be a thing. But there's been a flood of heterosexual men and women so damaged that if they dont fit into their gender roles perfectly, are chopping off their dicks or breasts and coming in to our community to go against the very essence of what we fought for which was that gender doesnt have to be tied to sex. (but they medicalize and pathologize any deviance from gender roles as meaning there's something deeply wrong with you and you must be of the opposite sex and need to change your sex to match a certain personality, which again, goes against the entire history of our movement)