Solar- This is a really good question. On the one hand, I would say the majority of Ts are not in the profession to work with clients who are copies of themselves. Yet, I do think that when there are basic commonalities, it can foster the relationship. Though you dont have to have these things in common to have a close relationship.

I know very little about my current T. I know she has parents in florida and a sister. And grandchildren about the ages of my kids. I dont know her religious views, her background (tho I suspect it is different than mine), her polititcs or where she lives. I do know she is married. When we talk in session we agree on things having to do with relationships and men. She guides me and I confide in her and trust her (for the most part). I dont have much of a desire or wonder about any of the other things. And, really, that is UNUSUAL for me. I think maybe b/c at this point, I am there to only have therapy and not really to heal through my close relationship with her. We were talking once about (mothers) and how she has clients who tell her they wish she was their mother. I did say to her that I dont see her in a motherly way for me. More of a peer. Or just a plain old therapist. It could be, but I dont know, that when I went to see her I was clear on the issues I needed help with. And f*** whether I trusted her or not, I just want to do the work and move forward. She seemed trustworthy enough.
Maybe all of this sounds a little cold. But it makes it easier to not be overly concerned with our differences. I was more concerned with her abilities to help me and her competence.