My daughter did not a have a best friend in Kinder, nor does she in 1st Grade- at this moment. I have seen the strain that can be placed when one of the bf's wants to venture with other friends and then one of them is not ok with it. This happened all through Kinder for one of the kids at our school and it was starting to change her personality. The other friend would cry and get emotional if the other friend wanted to play with other kids. One of the Mom's really wanted the two girls to be best friends, so that emotional want of the mom made it hard for the other mom, due to being friends with her. She was placing her own stuff on these Kinder girls. I would ask the teacher why she wants them separated? She may see another side to this as she is in the classroom atmosphere, and knows this age better than we do. Our school has a rule that no one can be excluded and everyone can play. It is enforced and it helps while they are so little. The BF concept is too huge for them to get at this young age. I can see the comfort for you mom's. The other mom did not like seeing her daughter go through the emotional stuff when the other little girl would cry, so she limited their play groups outside of school, and she invited other girls to come and play at their home to expose her daughter to other personalities.
Good luck with the teacher question.
Updated
I just read your response and my daughter is in First grade. Yes, this happens and it's so much earlier than I ever thought it would happen. Part of it is the influence if the child has an older sibling influence and we really have to monitor the TV shows that are watched. The kids can get their identity from it and what is said and acted on. First born children and only children tend to be younger, less mature. They don't have the day in day out learning behavior of sharing. It was hard for my only child at recess for awhile to learn that once she was playing at recess she had to let others play. I had to take deep breaths and let her learn some of it out there. It is a Life skill that is learned out there that we can't teach them, but guide them gently.