Final answer:
Student-led prayer at public school football games violates the Establishment Clause, as it implies school endorsement of religion, and such practices are prohibited to maintain church-state separation.
Step-by-step explanation:
The Establishment Clause prohibits public schools from endorsing specific religious practices, including student-led prayer at football games, as determined in the Santa Fe Independent School District v. Doe. This landmark case found that such practices violate the constitutional separation of church and state. Public schools must maintain a neutral stance on religion; voluntary, non-disruptive prayer that is not organized or facilitated by the school is permissible, but official endorsement or organization of prayer by the school's authority, including student-led prayer at school-sponsored events, is unconstitutional.
The case Engel v. Vitale further illustrates the principle that government-approved religious activities, even non-denominational, are not permitted in public schools. However, individual, private prayer remains protected under the Free Exercise Clause, provided it is not disruptive or school-endorsed. The delicate balance between maintaining religious freedom and avoiding the establishment of religion continues to shape policies surrounding prayer in public educational settings.