lara, 'I suppose anything these days can be labeled discriminatory'
Well, no, not anything, but something that impacts one group of people and not another IS clearly discriminatory.
The short-hair rule for men is discriminatory too, I'd say, as women are allowed short or long hair. If women had to have long hair and men short then that rule would be unfair on both genders, and somewhat old-fashioned in its assumption, but not discriminatory or sexist I don't think.
I appreciate that your company makes these policies clear and that it does allow flat shoes with a doctor's note (although I think that's pretty 
in itself. I've no particular problem with your company specifically from what you've told us; or, rather, the problem I have is that I think this is symptomatic of a wider attitude –that women look more attractive, or suitable, or smart, or whatever, in a certain height of footwear that comes with discomfort and potential health problems.
I said this before but I'll repeat it: there is no equivalent item of clothing,that I can think of, that is specific to men. That makes it a gender issue, a women's issue, a feminist issue, whatever you want to call it.