not to belabor the point, but there are some close parallels if you consider ‘women only’ swimming times at public swimming pools:
https://www.nytimes.com/2016/06/01/opinion/everybody-into-the-pool.html
I believe the legal question would be if having select women-only screenings would be ‘reasonable accommodation’, and i would think it probably is.
Nothing to see here except people who get mad at anything they can label political correctness.