Yes, schools should decide whether prayer is acceptable to their students. Some private schools are founded by religious groups with the purpose of providing a faith-based education. The country was founded on a principle of freedom of religion. It is wrong to impose secular values on an institution founded on religious values. Forbidding prayer is the same as imposing censorship.
Prayer in school is an issue in public schools. All public school students in the United States must be treated in a similar manner, according to the equal protection clause of the Constitution of the United States. For this reason, a piecemeal approach to the issue of school prayer would run afoul of the Constitution.
No, individual schools should not have the right to determine prayer offerings because court rulings have made it clear that the separation of church and state prohibit organized prayer in schools. The rules should not differ for a subset of students simply because they go to a school in a community that does not honor the court rulings.
The United States constitution disallows government or government institutions to take any action that demonstrates a preference for or against any religion. Prayer is demonstrating a preference for religion. Any public school that allows prayer is, therefore, violating the constitutional rights of students who practice those religions that do not worship the Judeo-Christian God or who do not practice any religion.