I would highly recommend getting a copy of the WPATH guidelines and familiarizing yourself with them and don't be afraid to question the therapist. I started seeing an LCSW for depression and I told her why - that I had gender issues. During our discussions I mentioned the WPATH guidelines and asked if she was familiar with them. She wasn't. Not a big deal since she was helping with the depression and exploring the gender issues knowledgeably. When I had to quit seeing her and asked for a letter to begin HRT and she asked how I wanted it to read. I asked her if I was her first transgender patient and she admitted I was. To me no big deal because she was helping with the depression and Gender Dysphoria.
So aside from the comprehensive list, the question is, "Are they helping?" If not start looking for a new one.
Also while most therapists do have non-disclosure agreements, there was a notice in mine that they may tell someone if they think we are a danger to ourselves or others.
Also, regarding the question about sex with men. She did bring up the question in our discussion about transition and post transition plans. I told her while I primarily was leaning towards lesbian, I told her I hoped to have sex with men as I had heard that natural dialation was the best method. Gave us both a good giggle. But to her, gay, lesbian or bi had no impact on whether or not she would give the letter or not. Which she did send me.