U.S. Supreme Court justices expressed doubts about a Tennessee law that imposes residency requirements on people seeking to run liquor stores, taking up a rare test of the 1933 constitutional amendment that repealed Prohibition.

Tennessee requires people to live in the state for two years to get a retail liquor license and for 10 years to get a license renewed.

Justice Brett Kavanaugh was among the skeptics at Wednesday’s argument, saying the text of the 21st Amendment “does not support” rules designed to protect local liquor retailers from out-of-state competition.

But Justice Neil Gorsuch was more supportive of the Tennessee...