Senator J.D. Vance of Ohio has accused President Biden of trying to inundate the heartland with fentanyl to “punish people who didn’t vote for him.” He has eagerly promoted the false claim that former President Donald J. Trump won the 2020 election. And recently, he announced his plans to block all nominations to the Justice Department until it stops what he describes as a “political prosecution” of Mr. Trump.

But on Tuesday, Mr. Vance spoke about a different gripe altogether: the relaxing of the Senate dress code, which he said would demean America’s governmental institutions.

“My grandfather, who I never saw wear a suit, who didn’t own a suit as far as I know, would have never shown up to work in the United States Senate without dressing properly,” said Mr. Vance, who grew up in poverty in Appalachia and today purchases his bespoke suits from an Italian tailor in Cincinnati. “A lot of working-class people across this country respect this building. They’re frustrated by it, but they respect it and I think the dress code should reflect that.”

The recent decision by Senator Chuck Schumer, Democrat of New York and the majority leader, to relax the Senate’s informal dress code and allow members to enter the chamber in casual attire, or even gym clothes, has set off waves of consternation and cries of dismay in the stuffy upper chamber. Many senators, mostly Republicans, have publicly expressed concerns along the same lines as Mr. Vance’s, and privately have said that the change could harm America’s standing on the international stage.

Even some Democrats say they are appalled. At the Capitol on Tuesday, Senator Joe Manchin of West Virginia, said he had told Senator John Fetterman, the Pennsylvania Democrat whose hoodie-and-gym-shorts attire appears to have prompted the change, that he thought the decision was “wrong” and that he would do everything in his power to “try to hold the decorum” of the Senate.

“Senator Schumer has done everything he can to destroy the traditions of the Senate,” said Senator John Cornyn, Republican of Texas. “It’s another indication he doesn’t respect the Senate as an institution.”

Senator Cynthia Lummis, Republican of Wyoming, said that “people who dress like slobs tend to think they can act like slobs.”

“We have a bad enough reputation for lack of civility and decorum now, and this just takes it to rock bottom,” she added.

Senator Susan Collins, the 70-year-old Republican from Maine who favors modest, tailored skirt suits, joked that she would protest by showing up to work wearing a bikini, an image so incongruous she didn’t have to say anything more. By the end of the day, 46 Republican Senators — the vast majority of the caucus — had signed a public letter to Mr. Schumer, imploring him to reverse the plan. “The world watches us on that floor, and we must protect the sanctity of that place at all costs,” they wrote.

The new rules, which direct the sergeant-at-arms to no longer enforce the longstanding dress code for members, appear to have been changed mainly to accommodate Mr. Fetterman. Since returning to the Senate after being hospitalized for depression, Mr. Fetterman has refused to squeeze his hulking, 6-foot-8 frame into a suit, navigating the Capitol instead in airy basketball shorts and oversized sweatshirts. The rule change will now allow him to enter the chamber, and even preside over it, in his preferred state of dishevelment, which doubles as a way to signal his blue-collar, outsider status.

“Oh my god!” Mr. Fetterman said sarcastically on Tuesday of the hand-wringing about what would become of the nation’s Capitol if he were to preside over the Senate in a hoodie. “I think it will be OK. The Republicans think I’m going to burst through the doors and start break dancing on the floor in shorts. I don’t think it’s going to be a big issue.”

Online, Mr. Fetterman has been having fun pointing out instances in which the Republicans who have criticized him for his sartorial choices have not comported themselves with great dignity or decorum, even while wearing business slacks or dresses.

Representative Marjorie Taylor Greene, Republican of Georgia, called it “disgraceful” that the Senate was “lowering the bar” by changing its dress code.

“Thankfully, the nation’s lower chamber lives by a higher code of conduct: displaying ding-a-ling pics in a public hearing,” Mr. Fetterman replied, referencing Ms. Greene’s move during a recent House committee hearing to display oversized nude photos of the president’s son, Hunter Biden, engaged in sex acts.

The dress code drama, however inconsequential it may seem during a week when Congress is inching steadily closer to a government shutdown, did ignite a real discussion about what it means to show respect for the body in which one serves — especially at a moment when hard-right members who feel they have been sent to Washington to dismantle the government and disrupt its hallowed institutions are wielding their influence.

To many, gym shorts may be a sign of disrespect. But many of the best-dressed members in Congress have not always acted in ways that convey respect for democratic institutions.

Representative Jeff Van Drew, the former New Jersey Democrat who switched parties in 2019 and pledged his “undying support” to Mr. Trump, shows up to work most days with a four-point pocket square. In 2021, he voted to overturn the presidential election results.

Representative George Santos, the Long Island Republican who has been charged by federal prosecutors with money laundering, stealing public money, wire fraud and making false statements to Congress, among other crimes, regularly looks preppy and dapper in his signature crew-neck sweaters layered over crisp, white, button-down shirts. Despite his natty outfits, his Republican colleagues largely treat him like a pariah who brings only notoriety by association.

Some members argued that it’s not lawmakers’ dress code, but their inability to address pressing issues of national import that draws disrespect from allies abroad.

Representative Jasmine Crockett, a freshman Democrat from Texas, said she spent much of the summer break on a bipartisan congressional trip to Southeast Asia, where leaders she met with in Thailand, the Philippines and Indonesia were mystified at Congress’s paralysis. “When we asked why our exchange numbers are down at universities, they talked about gun violence,” she said, noting that Congress has been unable to muster a bipartisan consensus to enact any additional gun control measures in response to an epidemic of mass shootings.

When pressed about why a dress code should matter so much in a political moment defined by “ding-a-ling” pictures, Mr. Vance laughed.

“We should set standards of behavior, recognizing that a lot of people, most people, will fall short from time to time,” he said.

Senator Sherrod Brown of Ohio was one of the few Democratic senators unhappy about the dress code and its attendant issues of respect for different reasons.

“I can go in dressed any way I want and the workers can’t?” Mr. Brown said, noting that the change would not extend to the staff members who work in the chamber. “If we are allowed to dress casually, they should be allowed to dress casually. To me, it’s a dignity of work issue.”