The appeals court that let an aggressive Texas immigration law come into force in a one-sentence order without a hint of reasoning has a reputation for issuing decisions too conservative even for the Supreme Court, which is itself tilted to the right by a six-justice supermajority of Republican appointees.

But the Supreme Court has for now let that order, which overrode a trial judge’s decision blocking the law, stand, indicating that it will not consider the case until the appeals court issues something more formal than a “temporary administrative stay.” The fate of the law, known as S.B. 4, remains uncertain, as the U.S. Court of Appeals for the Fifth Circuit, in New Orleans, is often out of step with the justices.

In dissent on Tuesday, Justice Sonia Sotomayor took aim at the appeals court. “The Fifth Circuit abused its discretion,” she wrote, “and this court makes the same mistake by permitting a temporary administrative stay to alter the status quo that has existed for over a century.”

She added: “The Fifth Circuit should have considered the constitutionality and irreparable harm caused by S. B. 4 before allowing the law to go into effect. Instead, it opened the door to profound disruption. This court makes the same mistake.”

Of the appeals court’s 17 active judges, only five were appointed by Democratic presidents. Six members of the court were appointed by Donald J. Trump when he was president.

The court hears appeals from federal trial courts in Louisiana, Mississippi and Texas. Those forums often attract ambitious lawsuits from conservative litigants correctly anticipating a favorable reception, and rulings from trial judges in those states are often affirmed by the Fifth Circuit.

But when those cases reach the Supreme Court, they sometimes fizzle out. An attack on the constitutionality of the Consumer Financial Protection Bureau, endorsed by three Trump appointees on the Fifth Circuit, did not seem to fare well before the justices when it was argued in October. Another, in which the Fifth Circuit struck down a federal law barring domestic abusers from carrying guns, was also met with skepticism.

Other rulings from the Fifth Circuit, on issues like immigration, abortion pills and so-called ghost guns, have also met with at least tentative disapproval from the Supreme Court.