I can understand your bf wanting to derive some kind of stable relationship with his ex rather than stay stuck in the trauma of the divorce. It is probably his way of moving forward from that time. The other thing is they were married and he loves her even if they ultimately proved incompatible. The love can be compartmentalized and made unreachable, but I have never known anyone (sane) to completely un-love someone. So wanting a positive relationship - a friendship - with her reframes emotions beyond the pain.
All of that said, you absolutely should not have to personally contend with her negativity. If I were in your position, I simply would choose not to interact with her in any way, shape or form.