Senator Bill Cassidy of Louisiana did not just vote this week with Democrats to proceed with the impeachment trial of former President Donald J. Trump — he also effectively shamed his fellow Republican senators by voicing, and acting on, what many of them were surely thinking.

Mr. Cassidy blistered Mr. Trump’s lawyers as “disorganized” and seemingly “embarrassed by their arguments,” explaining that their poor performance and the compelling case by the Democratic House impeachment managers had persuaded him to break from his party’s attempt to dismiss the proceedings on constitutional grounds.

“If I’m an impartial juror, and one side is doing a great job, and the other side is doing a terrible job, on the issue at hand, as an impartial juror, I’m going to vote for the side that did the good job,” he told reporters on Tuesday. He did, though, emphasize on Wednesday that his view on constitutionality did not “predict my vote on anything else,” namely whether to convict Mr. Trump, saying only that he had an “open mind.”

By becoming the only Senate Republican to switch his position from the one he held last month on a similar question about the constitutionality of holding an impeachment trial for a person no longer in public office, however, Mr. Cassidy delighted Louisiana Democrats, angered Republicans in his home state and presented himself as a one-man testimony of why Mr. Trump’s eventual acquittal is all but inevitable.

“There is literally nothing that the Trump lawyers could do to change any of these other Republicans’ minds,” said Senator Brian Schatz, a Hawaii Democrat. “They couldn’t have tanked it on purpose any worse than they did, and they still only lost one.”

That Mr. Cassidy was that sole senator to be lost, joining the five Republicans who also sided with Democrats in January on the constitutionality of the trial, may have seemed surprising at first glance. After all, he has been a fairly reliable conservative vote since being elected to the Senate in 2014, and Louisiana just handed Mr. Trump a 19-percentage-point victory over President Biden.

Yet Mr. Cassidy, a 63-year-old physician, also has an iconoclastic streak and can be quirky. A devoted fan of his alma mater’s football program, Mr. Cassidy can rattle off the precise number of Louisiana State University football players who have left college early to be drafted into the N.F.L.

One fellow Louisianian, former Representative Cedric Richmond, who in 2014 said that the “dude is weird,” put it more delicately on Wednesday. “He has always been independent,” said Mr. Richmond, a Democrat who served in Congress with Mr. Cassidy and is now a senior adviser to Mr. Biden, calling the senator’s vote a “profile in courage.”

Mr. Cassidy is part of an increasingly vocal group of red-state Senate Republicans who, having spent more time in their careers confirming judges than legislating, are eager to work with Mr. Biden and their Democratic colleagues.

Mr. Cassidy signaled his very public turn toward pragmatism less than a month after cruising to re-election last year by 40 points.

First, he became the most prominent Louisiana Republican, and one of only a few G.O.P. senators in the South, to acknowledge in November that Mr. Biden had won the election.

Then he left no doubt about his intentions with a decidedly Louisiana touch. He showed up at a Capitol Hill news conference in December bearing Mardi Gras beads to make the case for state and local aid in a coronavirus relief package, warning that cities like New Orleans were being financially battered without tourist dollars.

In joining a bipartisan Senate “gang” after his landslide re-election to push for what eventually became the $900 billion measure that Mr. Trump signed in December, a seemingly liberated Mr. Cassidy indicated that he would use his next, and perhaps final, six-year term as a constructive force in Congress for a state confronting profound economic, public health and environmental challenges exacerbated by the pandemic.

“I’m 63 years old, I am a senator because I love my country, I love my state, and I am going to work my hardest for my state and my country,” he said after that December news conference, adding with a shrug: “I want my state and my country to do well and what comes, comes.”

If that approach makes for a sharp contrast with Senator John Kennedy — his fellow Louisiana Republican, who delights in dishing one-liners on cable television — it puts him in league with an emerging group of G.O.P. lawmakers more interested in accruing legislative accomplishments than Fox News appearances.

This coalition includes some of the Republican senators who visited the White House to discuss the next virus package with Mr. Biden this month. Their ranks include not just moderate stalwarts like Susan Collins of Maine and Lisa Murkowski of Alaska but also more conservative lawmakers like Todd Young of Indiana, Shelley Moore Capito of West Virginia and Jerry Moran of Kansas.

“We’re looking for solutions,” said Mr. Young, who until recently was the chairman of the Senate Republican campaign arm and is eager to turn back to policy.

Mr. Schatz, who is friendly with some of these senators, put a finer point on their motivation: “If I’m going to suffer through the Trump era, then I may as well enact some laws.”

In Louisiana, though, the thoroughly Trumpified Republican Party expects only continued fealty to the former president.

Mr. Cassidy confronted immediate criticism for his vote and comments on Tuesday.

“I received many calls this afternoon from Republicans in Louisiana who think that @SenBillCassidy did a ‘terrible job’ today,” Blake Miguez, the State House Republican leader, wrote on Twitter, repurposing Mr. Cassidy’s critique of Mr. Trump’s lawyers. “I understand their frustrations and join them in their disappointment.”

Even a fellow member of the Louisiana congressional delegation, Representative Mike Johnson, weighed in. “A lot of people from back home are calling me about it right now,” noted Mr. Johnson, a Republican, who said he was “surprised” by Mr. Cassidy’s move.

Perhaps he should not have been.

As Stephanie Grace, the longtime political columnist for The Times-Picayune in New Orleans, wrote in a December piece anticipating Mr. Cassidy’s shift, he “has long been part of bipartisan efforts to solve problems, even if his solutions probably go too far for some Republicans and stop way short of what many Democrats want.”

Mr. Cassidy, a former Democrat like Mr. Kennedy and many Southern Republicans their age, has long been less than dogmatic on health care, a viewpoint he formed working in his state’s charity hospitals. This has always been more than a little ironic to Louisiana political insiders, given that in 2014 he unseated Senator Mary Landrieu, a Democrat, thanks to conservative attacks on former President Barack Obama and the Affordable Care Act. (On Wednesday, Ms. Landrieu said of Mr. Cassidy, “Many people in Louisiana are proud of him, including me.”)

Yet by 2017, during the heated debate over whether to repeal the health care law, Mr. Cassidy was warning that to kick people off their insurance or make coverage unaffordable would only shift costs back to taxpayers by burdening emergency rooms.

“If you want to be fiscally responsible, then coverage is better than no coverage,” he said at the time, conceding that Congress had established “the right for every American to have health care.”

Such remarks, like much else policy-related in the Trump era, were overshadowed by the incessant White House drama. But Mr. Cassidy’s turn toward the political middle isn’t lost on Louisiana Democrats now.

“He seems to be developing this moderate, deal-making persona,” said Mandie Landry, a state representative from Louisiana. “Kennedy has become so out there and embarrassing that it gives Cassidy some space, especially if he’s not running again.”

That was clear enough from the senator’s comportment on Wednesday morning, when he seemed to evoke the most memorable lyrics of the Louisiana-inspired song “Me and Bobby McGee”: “Freedom’s just another word for nothing left to lose.”

Happily striding to the microphone set up for television cameras in the Capitol basement to take questions, Mr. Cassidy acknowledged that the reaction in Louisiana to his vote had been “mixed.”

Then he continued.

“It is Constitution and country over party,” he said of his approach. “For some, they get it. And for others, they’re not quite so sure. But that’s to be expected.”