Hey there,
People go to therapy for different reasons, and like different types of therapy....so, for example, if you had someone who was doing cognitive behavioral therapy who assigned worksheets and homework, maybe it wouldn't matter so much.
Personally, I wanted much deeper, insight-oriented therapy that related to my relationships with other people. I could not have engaged in that with someone if I worried they would judge me for something so basic as my sexuality. Change requires taking emotional risks, and I would not be able to take risks with someone I did not trust.
Maybe it's worth taking this risk. Or, you could say, "I'm worried about talking to you about something because I worry you will judge and reject me. I even worry that this space is not 100% safe in terms of confidentiality." And see what he says.
Honestly, though, if he is a decent therapist with a good bit of experience, and you are talking to him about "a friend" who is really more than a friend and you feel weird and awkward, he may already have guessed your secret.