Hi Cami,
I have had similar issues working with, for and around the Catholic Church. Even though there are specific laws in my city, state and county that protect those with gender identity issues, and even though based on these laws I might be able to challenge what I perceive as unfair restrictions that the sisters put on health coverage profiles, I have chosen to keep quiet and fly under the radar as much as possible.
It did happen once that a therapist I was seeing several years ago took it upon himself to submit a diagnosis of gender identity disorder on an insurance claim. The insurance company immediately stopped paying for my hormones and began to challenge every medical procedure I presented for. When I contacted the insurance company (administered by a large female religious organization) I was told that gender identity related services were excluded from my insurance plan. I told them that the diagnosis was a mistake. They demanded full access to my therapy files. I flatly refused. Rather than fight with them, I just started paying out of pocket for my hormones and limited my doctor visits. Every time I picked up my medications from the pharmacy, the pharmicist would tell me that the insurance company denied my claim; I would say, "I know" matter of factly, and pay for my drugs.
This went on for about 10 months. And then suddenly, without any explanation, the insurance company started paying again, and they stopped challenging my every medical claim. They never told me why the change or heart, and I never asked. I never went back to that therapist, and no question of my gender identity has ever come up again with the insurance company or with the sisters.
Your mileage may vary, but I choose to keep this information very much to myself, and I choose my battles very carefully.
Good luck to you.
Miharu