I've had experience with 3 Ts: one male, my long-term T; and 2 females who consecutively ran a group. Both of the females had abuse backgrounds (long-term T did not). Both female Ts allowed their own issues to grossly interfere with the group.

Personally, I would never knowingly enter therapy with a T who shared my issues. I think any sense of affiliation or extra understanding is marginal at best, and destructive at worst. I think it's all part of a bigger problem that too many people in treatment or needing treatment seek to "help" people really from an inner need to help themselves and simply get in over their heads. It's also why I favor higher degrees as credentials because it weeds out some of these folks.

I do think character is important. For me, it speaks to authenticity and trust, and is more indicative than sharing a negative life experience.