The way I approached it was that I explained that I was in therapy to address some issues I have been having. During intense psychotherapy with a team of psychologists, they determined that I am transgender. The treatment for the issues, Gender Dysphoria, is hormone therapy. This was sent to my medical team, who agreed with the assessment and prescribed the medications.
This removes the concept that I "chose" this, that it is a fad, a fantasy, or any other "excuse". It is a medical treatment. I don't question their medical treatment for diabetes, so why question my medical treatment for any other condition?
The questions that followed were along the lines of this had something to do with how I was raised. Parents feel guilt when such possibilities arise. I assured them that it has nothing to do with the environment and is a genetic condition that science does not yet fully understand.
Therefore, the appropriate treatment, hormone therapy, is recognized and approved by over 25 of the top medical professional organizations worldwide.
Since my stepbrother is an MD and a former president of the Colorado Medical Society, they had to confer with him. He cannot dispute any of my claims, so my parents have accepted that this is what is happening. It took years for my dad to address me by my new legal name, but he only slips once in a while now, and I ignore it.
Hopefully, this will help you all have that discussion with your family and friends. Remember that it is nobody's fault. No one is to blame. It is a recognized medical condition, no different from diabetes or PCOS.