Is it possible to not react badly to a diagnosis of borderline/personality disorder?

Yes: While serious, i often find the diagnosis of bpd to be a relief for a great many patients. It explains an awful lot of issues and there is treatment for it. A great deal of diagnosing in general is about the delivery of 'bad' or difficult information to your patient in a professional and understanding matter. Bedside manner counts here.

Borderline: I have never heard of such a diagnosis received with any level of joy, to be sure. Because of the seriousness of such a diagnosis, getting a second opinion might be a worthy undertaking.