Are those peope who are bipolar get taken more seriously than those with borderline personality disorder?

Both disorders are : Serious and taken seriously by professionals and family members. I'm not sure why you think they are not. Please ask again.

Borderline/bipolar: Neither diagnosis gets taken more seriously than the other, it's symptom severity that is the key item. Specifically, you could have either of these with moderate symptomology, but the others' symptomology could be severe, and even suicidal. The latter should get taken more seriously, for obvious reasons.