Here's what I like having in common with my T:
age - just really don't want someone lots younger than me
married and being a parent - massively helpful to have this innate understanding of these elements of my life that are very difficult to explain to a single non-parent.
sense of humor - we laugh at each other's jokes

T being a religious person vs. atheist is helpful to me, then I don't have to explain why my faith matters to me. However, the T's actual religion isn't so important.

However, I'd have an issue if my T highlighted our differences (I voted for X, did you?), brought them into the therapy (veganism will save your life) or tried to change my core beliefs (lots of religious stuff on display). It would be very unprofessional.