The justices have allowed vouchers for religious schools and required equal treatment in tuition programs. But direct government payments to religious public schools pose a new test.

A decision to allow a Catholic school to become a publicly funded charter would profoundly impact American education, experts say.

The Supreme Court will hear arguments Wednesday in a blockbuster dispute over the nation’s first religious charter school, a case that critics say has prompted a “crisis of identity” in the school choice movement and that could vastly expand taxpayer funding for religious education.