I am happy you worked things out, but our problem is similar.
I have twin boys and one son gets invited and the other one doesn’t. The reason my one son doesn’t get invited is because he has eczema and the kids laugh at him and call him names. But I have spoken with my son and told him he is still special cause God made him and God does not make junk, he makes everyone special in their own way.
This has happened on several occasions. Also they have had birthday parties and I invited the whole class so as not to leave anyone out. Now they are both not invited to a certain chosen few. This has been going on for a few years.
So we have excluded these birthday parties and we have a party with the family. We go and have Pizza and go bowling or swimming at a pool.
The boys feel better about this cause we are a family celebrating their birthday together.
As for the kids in the classrooms that send invitations out and my boys don’t receive one they tell me they like the way we celebrate their birthdays better. My twins are 9 years old and this has been since grade 1 and they are in grade 4.