The court’s order Tuesday leaves no legal obstacle in the way.
The high court is weighing an emergency appeal from Trump asking it to overturn a lower court ruling.
A decision against the schools could mean the end of affirmative action in college admissions.
Similar restrictions were imposed in 10 other states, according to the Firearms Policy Coalition.
The group claims religious discrimination and violations of other rights, saying they were spied on solely because of their faith.
President Trump’s federal lawsuit remains alive.
A Supreme Court decision over the constitutionality of the Affordable Care Act will not be made until spring, so people will still be able to purchase a policy on the exchange for 2021.
The Supreme Court says it will decide whether President Trump can exclude people living in the U.S. illegally from the census count that is used to allocate seats in the House of Representatives.
The three-judge panel ruled after hearing brief arguments from both sides.
Thursday's opinion says the Supreme Court upheld the all-male draft in 1981 and that “only the Supreme Court may revise its precedent.”