How do you deal with schools that brush off teachers treating your child biasly?

There has been some false narrative created around my child.

There are girls in her grade that don't like her for upholding truth and justice. They have started alienating my child and asking other girls in their friend groups to not play with my daughter.

The teachers are taking their sides of the story labelling my child as a boss liar. My child is apparently boss for telling the girls to not lie and to not do things she believes is wrong.

So the girls have been getting my kid into trouble lately. Telling the teachers that my kid is making them do things they don't want to do.

I've asked my kid to stay away from them as there are other friends who share similar values who treat her better.

Fast forward to the upcoming birthday invitations. My kid has given them out to a few closer friends. The girl that lead the clique to alienate my kid was not invited. When she found out, she created this big drama resulting in my child getting in trouble from school for excluding this child. I felt the teacher was unprofessional and should not have involved herself into this drama. Ilwhen I raised my concern of how the teacher handled the situation, I was shutdown and case closed by the principal.

I recognize that this is such a small matter. But wondering if anyone has ever dealt with this type of incident or may be able to give me some insightful guidance on how I should have or should be dealing with this type of situation?

Thank you

Update: Wow - Good insight and perspective and that's exactly why I had to come here for guidance. I have learned that regardless of how I've advised my kid to be discrete with the invitations, girls her age can't always contain their excitement. My kid did not spread the news of her birthday party and did so at each friend's locker. It was others in the friend circles that unfortunately was too excited and shared the news. So my child was accused of spreading the news of NOT inviting certain friends. Understandable, the teacher needed to step in to stop whatever drama had arisen, I just don't agree with how it was done. But eye opening and lessons were learned! Goodness sake, it was my child's first ever birthday party. We will likely keep it very small next year and it sucks because I've never had birthday parties and was excited for both of us.