Schools should have a clearly defined and Ministry approved Charter and Mission Statement.
The school board should be entirely done away with.

The Charter and Mission Statement should clearly outline the purpose of the school.

For example, it might say: Preparing Young Minds For Careers In Industry Through Scientific Education.

By attending the institution, the parents should sign a document that outlines the school in a few bullet points. And they then have to sign their names, saying the accept and understand this.

There is nothing to say there won't be religious schools. Provided the teachings are vetted and politics is not being taught with public funds.