The school is using the parents...All about money...To my knowledge, all Catholic schools are open to the general public...
From my personal experience, yes, non-Catholics can attend a Catholic school. Part of the contract for being admitted to a Catholic school includes a certain amount being donated to the Parish attached to the school, putting money into the basket, so to speak. Also, a certain amount of hours spent helping with school functions. However, very few kids in my children's schools were not Catholic. Most of the children in the school came from the Parish family.
Sure, they are open to the public, but it is STILL a Catholic school. And Catholic schools do not make money, it’s expensive. Better to close the school than to compromise your faith.