I'll throw in my ha'porth on this. I'll also be upfront about my position, which I'm sure will surprise no-one. I am opposed to segregation. That's my "ideological grounds". So I'll tolerate it only when it's unavoidable due to social norms and I regard those social norms as being wrong. I won't jump to segregation as the first choice because it might be more convenient.
Sounds a lot of hassle. Raise your hand, ask for the box, write a question, put it in the box, have it be pretty obvious it was your question when the teacher then pulls it out.
A practical objection to desegregation, not an ideological one. The solution is therefore also practical - don't use a box in that way. Have a physical box available outside of class. Have a virtual "box" that can be accessed remotely.
Also, your preferred "solution" of segregation doesn't solve the problem you raise. You would still have children being identified as the asker of the question. In your system, the child would have to speak the question in class. That's worse than writing it down and putting it in a box, even if they're identified as the asker of the question in both scenarios.
Or do you think kids know what questions they'll think of before the actual talk? Do you think there will be a whole series of talks to make sure all questions are answered and you repeat in a loop until there are no more questions from the previous lesson? In sex education, which is embarrassing enough, you want to do everything you can do to make people feel comfortable asking questions.
That's a better point, but again segregation isn't a good solution to it. You're still making it necessary for children to speak up in class and ask questions in person. Ideally that shouldn't be a problem, but it is. Many will be too embarrassed to do so and therefore won't get an answer. Segregation might make some children somewhat less embarrassed about asking questions, but only because of segregation - the existence and promoting of segregation makes segregation expected and therefore makes people more comfortable when segregated. This might fall into my position of "I'll tolerate it only when it's unavoidable due to social norms and I regard those social norms as being wrong."
(EDIT: looking through later posts in the thread, I see someone has already suggested a practical solution to both those practical problems - give every child a piece of paper to write on and have every child put it in the box during the class, so it becomes impossible to know which child asked which question)
Separating boys and girls is a very simple and immediate way of helping achieve that for both boys and girls. I suspect you are against it mainly on ideological grounds. If you are worried about boys not learning about menstruation, explain to me why that wouldn't be included in the boys class also.
Segregation doesn't lend itself to inclusion. It's
possible to be inclusive in what's taught while being exclusive on the grounds of sex/"race"/whatever, but it's unlikely. It's also unlikely that there would be a lack of bias - "seperate but equal" doesn't exactly have a good track record.
More importantly to me, I think that segregation is itself a bad thing to be teaching children. Especially sexual segregation when teaching about sexual relationships. The mismatch is particularly bad for that, given that most sexual relationships are heterosexual, i.e. very much not segregated by sex.