I've found liability a huge factor in that. Even if the individual T is ok working with "high liability" clients, the agency they work for may not be.
I try to be upfront with new T's about my sui issues, my self-harm, my history with intensive mh care, and my trauma history. I don't necessarily parrot off the various diagnoses I've recieved over the years, but I am up-front about some of the things I consider "challenging" to work with. I have not had T's outright refuse to do an initial interview, but I have walked out of a few offices based on their reactions.
I don't see the benefit in not diclosing my sui/sh/trauma/refusal of meds. Yes, it may make finding a T more difficult, but at least I know I have not wasted my time building trust with someone that will over-react or freak out when that stuff does come up.
There's a lot of stigma around bpd and chronic sui ideation. I would prefer knowing where any potential T stands with that...