President Trump may have won a partial victory at the Supreme Court this week, but other federal judges remain major stumbling blocks to his aggressive immigration plans, with courts from California to Michigan and Atlanta limiting his crackdown on sanctuary cities and stopping him from deporting illegal immigrants he has targeted for removal.

The judges in those deportation cases have rejected Mr. Trump’s argument that he has wide latitude to decide who gets kicked out, without having to worry about district courts second-guessing him on facts of the case.

Instead, the judges said, they get to decide their jurisdiction, and that extends to reviewing Mr. Trump’s immigration policy.

One judge in Michigan ordered the Homeland Security Department to freeze all deportation plans for about 200 Chaldean Christians arrested over the past two months and scheduled to be sent back to Iraq. Nearly every one of them has a criminal record.

A judge in Atlanta ordered the department to reinstate the temporary deportation amnesty — known in governmentspeak as the DACA program — for Jessica Colotl, an illegal immigrant Dreamer whose past made her a target for deportation, officials said.

“The public has an interest in government agencies being required to comply with their own written guidelines instead of engaging in arbitrary decision-making,” said Judge Mark H. Cohen, breaking new ground in establishing legal rights for some illegal immigrants.

On Tuesday, a federal judge in California ordered the Border Patrol to improve its treatment of illegal immigrant children caught sneaking across the border. She said she was troubled by stories from illegal immigrants who said they were kept in dirty rooms without private toilets and sometimes had to wait up to 12 hours for their first meals.

When they were fed, it wasn’t enough, concluded Judge Dolly M. Gee.

Judge Gee ruled that the Border Patrol must provide the children with soap, toothbrushes and toothpaste, and access to showers.

Notably, all four of the judges — including one in San Francisco who blocked part of Mr. Trump’s executive order against sanctuary cities — were appointed to the bench by President Obama.

“Almost all of the judges are acting outside of established law,” said Hans von Spakovsky, a senior legal fellow at The Heritage Foundation who served as a Justice Department lawyer in the Bush administration.

For David Leopold, a former president of the American Immigration Lawyers Association, the judges are heroes upholding the Constitution when the political branches of government won’t.

“You’ve got the Republicans playing ball in the Senate and the House. The only institution that’s putting a check on this guy is the judiciary,” he said.

The Trump administration is fighting all the rulings but has had little luck convincing lower-court judges of Mr. Trump’s powers on immigration.

Mr. Trump, though, has had success at the Supreme Court, which issued a 9-0 decision this week reviving part of his travel ban executive order, which imposes a 90-day pause on some visitors from six majority-Muslim countries and a 120-day halt to all refugee admissions.

Reversing several lower-court rulings — all also issued by judges appointed by Democrats — the Supreme Court said Mr. Trump could stop refugees and visitors when they don’t already have “bona fide” close connections to people or entities in the U.S. For those who do have close connections, however, they have rights that must be respected.

Homeland Security is working out how it will interpret those directives, but analysts are deeply divided on what it means and whether the justices delivered a message to lower courts to back off their criticism of Mr. Trump.

Where lower-court judges pored over Mr. Trump’s campaign statements and perused his Twitter account looking for evidence to use against him, the Supreme Court took the president’s executive order at face value.

“The Supreme Court treated this like a normal case, like a normal executive action. So certainly this has to affect — probably not all judges, but certainly some,” said Ilya Shapiro, editor-in-chief of the Cato Institute’s Supreme Court Review.

He said that could set the stage for a return to the posture of the Obama years, when many of his actions were challenged in court but were greeted with seriousness by the judges who heard the cases — what legal scholars have come to call the “presumption of regularity.”

“I don’t think we’re there yet,” Mr. Shapiro said. “The [president’s] constant tweets — not just about immigration but lots of things — feed the fire of the resistance.”

Mr. von Spakovsky called the Supreme Court ruling “a slap in the face” to the judges who ruled against the broad swath of the president’s immigration plans.

“These judges are clearly hoping these cases don’t get appealed, don’t get to the Supreme Court, because if they do, they’re going to get overturned,” he predicted. “The lesson to them is they need to quit making political decisions based on the fact they don’t like the president and his policy, and start making legal decisions that follow binding precedent.”

Some analysts said the key part of the Supreme Court’s ruling was showing deference to the president’s national security decision-making. The justices said his judgment had to carry weight, particularly when it came to people who don’t have a connection to the U.S. and therefore don’t have constitutional rights to be weighed.

The court will hear broader arguments in the travel ban case in October.

Mr. Leopold said he initially saw the ruling as a loss for immigrant rights advocates, but after rereading it he concluded it’s a major win for his side and a slap at Mr. Trump.

“This is a rebuke,” he said. “They weren’t harsh in their words. It was very professional … But if you read between the lines, they basically say, ‘No, no, we’re not going to defer to you on national security here.’”

He also said the ruling is much more limited in empowering Mr. Trump than it might seem and that few people will be snared by the part of the executive order that the court revived, targeting those without close connections to the U.S.

But on Wednesday evening, the State Department issued a new set of visa guidelines to U.S. embassies on the six affected countries that was much narrower than immigration advocates might have hoped.

Refugee agencies argue that most refugees already in the pipeline have close connections because their names have already been forwarded for placement in the U.S. Immigrant rights advocates said anyone with a job offer, a relative living in the U.S. or who are part of a school program will also be exempted.

Advocacy groups said earlier Wednesday that if they thought the president was being too stingy, they would head back to the courts and likely the same lower-court judges who first ruled against Mr. Trump.

Mr. Leopold said that, far from being chastened, those judges will now feel emboldened by the Supreme Court.

“I think it stiffens the spine because they’re looking at this and they’re basically being upheld on the injunction,” he said. “Those judges have not been overruled.”

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