@TedMullins women and girls are at far greater risk in mixed sex changing rooms, regardless of the trans issue. Figures show far greater number of assaults there. It's not a solution.
As for the smear test... Look, I think for me this is where the difference between theory and reality comes in. Imagine you request a female practitioner, and in comes a burly six footer with an Adam's apple, asking you to remove your knickers and open wide. Honestly, how do you think most women are going to feel in the moment? Whose needs are more important in this situation?
Obviously some women might be perfectly happy to have their smear test done by anyone, male, female, trans, whatever. I've certainly had plenty of gynaecological procedures done by male doctors (sometimes a team of them!) and I didn't mind.
But some women, for all sorts of reasons, do mind.
There was a to-do in Scotland recently about intimate exams for rape survivors. The government initially said they could only request it to be done by someone of a specific gender, not sex. An MSP called Johann Lamont successfully argued to change the wording as follows: for the word gender, substitute sex. That's a good example to look up to read about the arguments either way.