In the space of two weeks, President Trump threatened to halt a congestion pricing program intended to reduce traffic in New York City and intervened in California as it confronted ruinous fires, overruling local officials as he made decisions about how to manage the state’s complicated water system.

He signed one executive order cutting off federal aid to elementary and high schools that allow transgender athletes to play in women’s sports, and another intended to end funding to medical institutions that use puberty blockers or hormones in gender-affirming treatments. On Thursday, his administration sued the City of Chicago and the State of Illinois in federal court, claiming that sanctuary laws are obstructing the federal government’s ability to enforce immigration policies.

For decades, the Republican Party, more than the Democratic Party, presented itself as an advocate of federalism, yielding authority and power to state and local governments. But this once-central tenet of Republican thought has seemingly been scrapped, with little debate, as Mr. Trump remakes the Republican Party in his name.

“Republicans believe in federalism, of deferring to the states and the government closest to the people,” said Karl Rove, who was a senior adviser to President George W. Bush. “Not clear how much he shares that view.”

The president’s attempt to dictate actions by the states — particularly the blue states — is the latest instance in which Mr. Trump has scrambled what remains of Republican orthodoxy. He has forced the party to abandon some of its ideological foundations on questions of foreign policy, deficit spending and, increasingly, respecting the rights of states to govern themselves and resist federal intervention.

“Federalism was certainly the orthodoxy in the Republican Party from the 1960s on,” said Max Boot, the author of a recent biography of Ronald Reagan, who as president advocated sending power to the states. “If a Democrat were doing this to red states, Republicans would be screaming bloody murder.”

Stephen K. Bannon, who was an architect of Mr. Trump’s victory in 2016 and who described himself as a strong proponent of federalism, said he was surprised that traditional Republicans had not raised concerns about some of the actions taken by Mr. Trump.

“I haven’t heard one peep about this,” he said. “Normally, federalism is a big deal. In the old days, there’d have been a big debate.”

Mr. Bannon said it was too soon to tell if this signaled a shift in Republican thought on the balance of power between the states and the federal government. “People have come to the conclusion that we have such a crisis in government,” he said. “People are totally focused on that. All the arguments about federalism are taking a back seat right now.”

Democrats have traditionally had a more unified view of federal power. They openly embraced the use of federal law — and often federal money — to influence a wide range of states’ policies, including on civil rights, voting rules, environmental regulations and even speed limits.

Some of Mr. Trump’s actions have used a familiar enforcement mechanism: threatening to cut off federal funds to states, local governments and school districts that do not comply with directives spelling out the administration’s policies on health care, the environment and energy. Many of the orders have been directed at the two biggest Democratic states: New York and California.

“Why does he want to stop offshore wind in California, if California wants to do it?” said Jerry Brown, the former Democratic governor of California. “Why does he want to stop electric vehicles if California wants them? He’s putting his White House view over the view of local governments. It offends the basic American structure of government.”

Michael Steele, a former Republican national chairman, who has become one of Mr. Trump’s leading critics, said the administration’s efforts to crack down on so-called sanctuary cities, which provide shelter for undocumented immigrants, ran counter to the traditional Republican view of the balance of power between Washington and local governments.

“The fact that this administration and Republicans on Capitol Hill are annoyed that a city within a state decides that it wants to provide sanctuary, regardless of their status — that is wholly within the purview of federalism,” Mr. Steele said. “That’s for them to decide. That is not a federal question.”

Many of the orders are certain to be challenged in court. Mr. Trump has turned to executive orders because it would most likely be difficult for him to go through a narrowly divided Congress.

To a considerable extent, the Republican Party’s adherence to federalism has wavered over the decades, depending on the political climate and the issue at hand. In 2002, Mr. Bush signed the No Child Left Behind Act, which required public schools to test students in reading and math annually. The schools faced penalties, including a loss of federal funds, if their students did not display measurable progress.

Similarly, some Republicans have long sought a national ban on abortion and used federal law to try to limit access to the procedure.

Mr. Trump’s federalism has also been situational. He celebrated the overturning of Roe v. Wade, which established a federal right to an abortion, as a win for states’ self-governance. And he has declared that he wants to eliminate the Department of Education, for decades a symbol of federal overreach.

But in the weeks since he moved back into the White House, Mr. Trump has proved to be far more aggressive than his predecessors from either party in seeking to mold state policy. And he has encountered little resistance from Republicans in Congress who have overwhelmingly supported what he is trying to do, regardless of their views on how he is trying to do it.

“I don’t think he has a moment when he thinks about federalism,” said Bill Kristol, a conservative commentator and publisher. “I think his instinct is, ‘I want to do this, and thus we want to do it to the whole country.’”

Mr. Kristol said he had agreed to serve as the chief of staff to the Department of Education in the Reagan administration, despite his own opposition to the creation of the department, because he was confident that the department under Mr. Reagan would never impose a federal curriculum on local schools.

By contrast, a week after taking office, Mr. Trump signed executive orders to block schools from teaching about “white privilege” and “unconscious bias,” and from recognizing transgender identities.

“You could say it’s a break from Republican orthodoxy,” Mr. Kristol said. “But that orthodoxy doesn’t have a lot of followers anymore.”

While the Democratic Party has over the years embraced an assertive view of federal power, there have been some prominent Democratic dissenters — including one from California.

“The federal government is not in the classroom,” Mr. Brown said. “It’s not in the state. It’s 3,000 miles away. That’s why you have 50 states, thousands of cities.”

Mr. Boot noted that Mr. Reagan, who was the governor of California before he became the president, had pushed to send federal money as block grants to states so that they could decide how to allocate it.

“But in more recent years Republicans have begun to embrace federal power as an instrument of social engineering,” he said. “I think it’s safe to say that for a lot of Republicans, their support for federalism was always more a matter of convenience than of deep-rooted conviction.”