I always see the facepalm icon and this is the first time I was temped to use it.
I'm very biased here because this person you are speaking of is a friend of mine.
I think there are so many factors. Who were you friends with longer? How long have you been with significant other? etc.
In general I think eventually you have to respect your significant other's wishes if it is a simple case of don't like the other person. If there are reasons you disagree with then you have to voice them to the significant other and see how things wind up. But if it is just "I don't like that person", you are doomed to fail if you don't respect those wishes.
However, not being friends does not mean to become that person's enemy as well. Very big difference here. If I like someone but my wife hates them, I will not hang out with said person anymore. But I will not throw stones at that person. I may even still consider them a friend but just cut all communication/ties.