Well the way I see it, neither sex ed nor biology is really the place for talking about transgender issues anyway. Sex ed is about sex and perhaps orientation and that has nothing to do with being transgender. And biology is about...well....biology. And they tend to refer to genitalia as male and female as opposed to men and women anyway (although teachers may mess up there - books tend to be more specific about this).
I think there should be acknowledgement of trans issues but I think it should be something specific as in visiting organisations or an assembly/separate class. It just doesn't really fit into any specific curriculum based class. To lump it in with sex ed wouldn't even feel right to me. Sex ed in general still applies to us in terms of sexual health and perhaps even sex orientation (if you're not in some backwards state/country that thinks that telling children gay people exist makes them gay...because that's how it works, of course *face palm*).
I think there's definitely room to evaluate gender norms and fight the binary, and at least make people aware of trans issues and that it's perfectly normal to be trans. In my school we had two classes, PSD (Personal and Social Development) and R.E. (Religious Education) and those are the classes where we'd discuss such issues. Our R.E. class was more about learning about other religions and atheism and being free to state opinions, even if they went against the Roman Catholic faith. And talking about current or big issues like euthanasia, abortion, the death penalty, etc. My school was Roman Catholic but in the UK, state schools can be specific religion schools but they're not allowed to require that students be of that faith; which is good when you're an atheist! Haha!
I think it belongs where it's not curriculum learning, but it's more an open, respectable discussion where kids can state their opinions within reason. Sort of like here where generalisations can't be made but I statements, without offense caused, would be used. Like there would be set issues and the teacher would state the issue and have information on it and the kids could ask questions.
As for biology classes, the best way to handle them is realise that it isn't talking about men and women; it's talking about male and female. The way I view it is that we're men who were born female. We weren't born girls, just born females. I look at that and define that as female = my anatomy and chemical structure, it doesn't equate to gender. Gender comes from my brain. There's a huge difference when you view it like that. It's not great to be reminded that you don't have a penis, yeah, but at the same time, you take a shower and you're reminded. You get dressed and you're reminded. You reach into your pockets and you're reminded. You go to the bathroom and you're reminded. This is just one more reminder, and it's all information you do need to know about to learn about safe sex, reproduction (important in biology course) as well as realise all the differences and understand what's possible and attainable for yourself in the future if you did decide this was something you wanted to change.
As for getting out of class, it's not going to be possible in a biology class. You can get our of sex ed but in a biology class, you can get tested on this stuff in the exams. There can be a picture and you have to label it, or you have to describe the stages of reproduction. So I would personally suggest removing men/women from your mind and assigning it to just male/female. It may help.