WASHINGTON — The Supreme Court on Monday let stand an Arizona program that aids religious schools, saying in a 5-to-4 decision that the plaintiffs had no standing to challenge it.

The program itself is novel and complicated, and allowing it to go forward may be of no particular moment. But by closing the courthouse door to some kinds of suits that claim violations of the First Amendment’s ban on government establishment of religion, the court’s ruling in the case may be quite consequential.

Justice Elena Kagan, in her first dissent, said the majority had laid waste to the doctrine of “taxpayer standing,” which allows suits from people who object to having tax money spent on religious matters. “The court’s opinion,” Justice Kagan wrote, “offers a road map — more truly, just a one-step instruction — to any government that wishes to insulate its financing of religious activity from legal challenge.”

The decision divided the court along the usual ideological lines, with the three other more liberal members — Justices Ruth Bader Ginsburg, Stephen G. Breyer and Sonia Sotomayor — joining the dissent.