The word is “homophobia.” Bigotry based on minority sexual orientation. Bigotry against LGBTQ people.
“Heteronormativity” is not right because that is only one kind of homophobia. There are other kinds like stereotyping and gay-bashing.
By rejecting the word “homophobia,” you are actually being heteronormative. You are saying that hetero people can define what is normal and just reject the actual word for bigotry against LGBTQ people because they don’t like it, and then define some other word. This is a very common trap to fall into.
The word “homophobia” is not literally designed in such a way that it will please your grammatical sensibilities. The word was coined by regular people, not by language designers. It started out as slang, like many English words. And English doesn’t have language police that would make sure literary rules are followed anyway. Many words deviate from the Latin rules. It doesn’t have to deconstruct well.
So you can’t literally focus on the “homo” and assume it only applies to homosexuals and not to bisexuals for example. Bisexuals also engage in homosexual love. But even that is too literal. The scope of the word has progressed to be more inclusive in the same way that we keep adding letters to the very-inclusive LGBTQ community. The same as “gay-bashing” applies not only to gay men but to any LGBTQ person who is beaten or killed for who they are.
Yes, many asexuals consider themselves to be part of the very-inclusive LGBTQ community. Again, it is not academic logic or grammatical sense that determines this, it is the fact that the LGBTQ community is welcoming and inclusive and protects asexuals from gay-bashing by heterosexuals. And the fact that asexuals themselves have identified as part of the community.
No, you don’t get to judge whether “phobia” is appropriate. Again, it has roots in slang, so there is no argument to be made against it. But if you want to have that argument, yes, bigotry comes out of fear.
No, it is not positive to stereotype people, even if you yourself judge the characteristics you are assuming someone has to be positive. A stereotype of a gay decorator with great taste says it is maybe OK to be gay if you are a decorator and makes gay soldiers and truckers and politicians invisible.
Understand that for every LGBTQ person who fits your various stereotypes, there are 10 more who “looked straight” to you that you never noticed. And all 11 resented your stereotyping and the detrimental effect it has on everybody — even the person doing the stereotyping.
Make a sentence with “left-handed person” and you can substitute “LGBTQ person” in there. The fact that someone is left-handed or LGBTQ tells you absolutely nothing else about them. Same as the amount of pigment in someone’s skin tells you nothing about them. If you make assumptions about a person based on their handedness or sexual orientation or pigmentation it is always, always negative.
Finally, you can see Nichole’s answer:
Bigotry. The word you are looking for is bigotry.
… and Fiksdal’s comment:
Fair enough, but I guess you would have to add to it, such as “sexual orientation bigotry”
Sexual orientation bigotry: “homophobia.”