If a black child was being called the N word everyday at school would you be insisting that the child just learns to cope with it, or would you be at school all guns blazing insisting on exclusion for the perps, going to governors etc?
The difference is that the OPs daughter was not called gay. She was asked if she was gay. But the school have said they will deal with it. If my child was called the N word or gay, I may or may not complain but I wouldn't be naive enough to think that they can stop it happening completely. Kids can be horrible. It's not right but it is happening and has always happened. I have one child who doesn't let things bother him and another who is very, very sensitive and I know who life is easier for. I reluctantly accept that teachers can't stop every nasty child so the next best thing is to equip my child the skills to get through until they no longer have to deal with them.
She doesn't see why she has to learn about it, believes you can love whoever you want to love, be whoever you want to be but that you can't change sex."
But the lesson was on respect. She hasn't been told you can change sex, has she?
In my child’s case it was much more in his interest to move schools away from it
This is sometimes the best thing for some children. I have a couple of friends who home ed because the one size fits all school system didn't work for their children for various reasons. Schools and children are much the same everywhere so moving schools didn't work.
You've repeatedly positioned the issue being with the child's feelings rather than problematic external issues.
If you mean the LGBT lessons, I wouldn't call them problematic. I am in favour of them. I have never come across any school that has said people can change sex, swap chromosomes or a boy liking pink must be a girl. These books and resources may exist but schools I know of are acknowledging trans people and trans issues but not saying anything about changing sex.