I genuinely think that in a professional medical setting, people should be viewing it as a job title rather than a gender anyway. It's more like a mechanic checking a car... It's very rarely comfortable being checked over in any way but you just do it and get on with it?
I think it's fair enough, from a safety point of view, for there to be two staff present for certain procedures and for example to request a 2nd staff member with gender of choice to sit in. To be honest it would be a good idea for that to be standard. Other than that... Surely the most important thing is having the most qualified people for the job checking you over? I guess I see it as, when you step into a clinical setting, they are doctors / nurses. Not males / females / transgendered or whatever.