I would dare to say that our job is to teach our children how to protect themselves.
I am way behind you at this, just starting with my toddler, but I try to think of the behavior that would best benefit my son and explain to him how to put it into practice.
With this parent, I would think how I would want my child to react to and act the same. If I think my child should not bother listening to them being mean, I would do the same. If I think my child should let them know their opinion is unwelcomed and unsolicited, I would do the same.
Again, there are instances when we tell one thing to the other parent and a different thing to our child, but I assume this is no longer the case with your child.
You've said it yourself that your daughter got tired of trying. Why would you exhaust yourself trying to make that parent understand anything?
Would I force myself to befriend my child's friends' parents? Only if it benefits my child.