While I am happy to admit that there are some transgender women who look very much like they were born women, the vast majority look like men in drag.
I'd love to see a citation for that claim. From what I've seen (both in papers and personally) most current transsexuals look very much like women. The issue is, they pass through their lives and no one questions them -- and they definitely don't want to "out" themselves as transsexuals -- so the ones that people think of as "transsexuals" is your stereotype.
If a 6 feet 4 "woman" with a square jaw and stubble walks into the changing room, it is quite reasonable that some women would be intimidated, irrespective of their genitalia (which they are presumably not exhibiting anyway the moment they walk in).
I disagree -- from what I know it should be extremely rare for a post-op woman to have "stubble." I'm guessing more genetic females have facial hair and "stubble" than transsexuals -- I'm sure you've known older women who have gravely voices and "stubble."
As for 6'4", I'm guessing many woman would be "intimidated," and may even make false assumptions, regardless of the genitals of that 6'4 woman at birth.
Beyond that, at least from what I know of the topic, transsexual females that don't "pass" well (look like men in drag) avoid dressing rooms like the plague. They know they don't pass well and don't want to call attention to themselves.
I am also happy to concede that the threat felt may be (and probably is) entirely imaginary. But that doesn't matter. If I went into a woman's changing room, any threat I posed would also be imaginary, but I think it would be entirely reasonable for the women to object.
But beyond that, your entire "straw man" here is pointless. The topic of this thread has nothing to do with "men." These transsexuals who are high school age should be able to pass very well -- if not it is because they haven't received the treatment they should have.
Having said that, I do think some of the transsexuals want to push this too far. I do think, for the school to recognize a student as transsexual, that the student/parents should be required to provide medical certification that they are undergoing treatment. Additionally, I think transsexuals should be excused from any activity, such as gym, that would require them to use changing rooms -- they can tell other students they have a medical condition that prevents them from taking gym class.
I do think, as a general rule, they should be allowed to use the bathroom of the gender they are presenting as. I realize that in cases, such as a school where doors have been removed from bathroom stalls, that there may be some type of accommodation made. Those accommodations; however, need to keep the student from being "outed."