I know people with BP. As long as they take care of it by following whatever treatment they need then it is ok. Same as depression or anxiety, if they do their part I am ok dating them.
To all honesty I would probably not date people with schizophrenia, am not sure of BPD.

My BF has severe OCD ( has to be medicated), GAD, ADD and Tourette's. None bothers me, just a bit of adjustment. He does his part to keep it in check. It doesn't effect his personality or moods, just some behaviors that I can deal with.

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