One thing I wanted to clarify about my earlier post...I don't think therapists HAVE to reveal personal details of their lives, other than those that directly impact therapy, but I DO think I have a right not to work with therapists who won't disclose certain things when asked (like religion, political leanings). I have no desire to work with a "blank slate" therapist and appreciate those that will show up more real and human in the relationship. I also appreciate those who are willing to equalize power as much as possible, and self-disclosure (especially when asked, and especially of identities and cultural dimensions) is one important way to do that.
So, I don't think therapists are obliged to share things other than those that directly impact therapy, but neither am I obliged to simply accept that and continue working with them if they won't.