Decide what, exactly?
Sex education curricula? That's school boards, and often Departments of Education whether State-level or federal.
Denying kids proper education can be a form of intentional neglect and abuse.
This is such a simple question to answer, when the answer is "the same people who make the other decisions about educational curricula".
If you, as a parent, have an issue with your kid learning that gay and trans people exist, you're just a bigot and you don't have a valid position. The same class of parents who whipped rocks at Ruby Bridges' head. They didn't have an argument, either, they were just hateful bigots who didn't have a problem assaulting a child.
This is essentially just an admission that your point of view is fundamentally hateful bullshit, and you know it. On most of these topics, there really aren't any legitimate "debates". They're bigots screaming that representation and support for people of differing identities exist, and everyone else telling them to stuff their hate, because hate is never a basis for debate.The deeper fundamentals are banned topics, so we can't explore the (likely) several ways that your hatred towards and projection onto conservative ideology relies on labeling and dismissing real topics of debate in gender identity, sexual preference, and LGBTQ issues. But nice all-caps closer for what it's worth.
I really don't care why you would want to exclude LGBT materials from classrooms. That you would want to is bigotry, based on nothing but hate and fear. There isn't another source for such views.
But, in the interest of fairness, I'm willing to entertain it. Make your case. As long as you're ready for me to break it down once you do. I'll take a refusal to do so as an admission that you know what you're doing.