I also work for a catholic based medical system. I can say that the dress code that they had adopted prior to my employment can be a double edged sword.
I guess that I was a bit fortunate that my primary care doctor is a member of this same system. I wore a bra full-time before she became my doctor and yes, my bra and gynecomastia was covered. I told her how wearing a bra improved my lifestyle and she agreed that a bra was a good option for dealing with ( at the time) were 38G/H breasts.
A few years later, I was employed by the same medical system, in all places, the Breast Care Center. They didn't have much of a choice in the matter that a Dr, had stated in my records that my bra provided pain relief and helped manage my gynecomastia. As my medical record recommended, they couldn't prevent me from wearing a bra anymore than they could say that I couldn't wear a knee brace.
Taking that same logic, I presented as male and I wore what was perceived as an article of clothing that was for women only, they could not deny any other clothing. I did not push the issue with wearing a skirt to the office as a man but, the dress code was changed and said something like "variances from the policy would be handled on a case by case basis. It was determined that a bra was a "reasonable accommodation " as stated by the Americans With Disabilities act.
❤️Sophie❤️