State dinners are useful tools for celebrating the culture of the visiting leader, so on Thursday evening, President Biden and the first lady, Jill Biden, hosted a 400-person soiree replete with sequins, saris and saffron-colored flowers in honor of Prime Minister Narendra Modi of India.

Meatless delicacies and sweet treats, like rose-cardamom strawberry shortcake, were offered to please the vegetarian guest of honor. The two leaders joked soberly — literally — about their relationship.

The good news, Mr. Biden said, was that “neither of us drinks.”

Holding a glass of ginger ale, Mr. Biden went on to toast “two great nations, two great friends, and two great powers.”

Still, the bitterness of political discord, both global and domestic, was detectable just beyond the White House gates. Outside, protesters stood in the rain, hoisting signs criticizing Mr. Modi’s treatment of religious groups. On Capitol Hill, House Republicans had just voted to start investigating the possibility of removing Mr. Biden from office over his immigration policies. The guest list included at least one other impeachment target: Alejandro N. Mayorkas, the secretary of homeland security.

The mix of political adversaries and Biden family members created a dinner scene so dissonant that no amount of glass clinking could have drowned out the partisan undercurrents.

Still, two prominent Republicans appeared at the White House and signaled they were putting their boxing gloves away for a few hours to enjoy the state dinner, which might be the only social invitation left in Washington that everyone still wants, political convictions be damned.

House Speaker Kevin McCarthy of California and Representative Steve Scalise of Louisiana really didn’t seem to want to talk politics. Mr. McCarthy, asked about the political machinations that seemed to have been switched off for the occasion, pointed out that he’d brought his daughter-in-law to the event — “It was my turn,” she told a crowd of reporters brightly — a tactic similar to the one he deployed when he took his mother to the state dinner in honor of Emmanuel Macron of France last winter.

Senator Chuck Schumer, the Democratic majority leader, was also disinclined to talk politics, steering reporters to his daughter-in-law, Elizabeth. Mr. Schumer ended up at the head table with the president and first lady, as did the fashion designer Ralph Lauren, who designed Dr. Biden’s sequined green gown.

Senator Joe Manchin III, a centrist who is often the legislative thorn in his party’s side, strode by with a smile on the arm of his wife.

Mr. Scalise, who previously scored an invitation to the Macron dinner, attended solo, and said only that he expected an “interesting dinner” given the hodgepodge of a guest list.

He was referring to the presence of Attorney General Merrick Garland and Hunter Biden, the president’s son who, two days earlier, signaled that he would plead guilty to two misdemeanor tax crimes and strike a deal to avoid prosecution on a gun charge. The younger Mr. Biden avoided reporters altogether, arriving by trolley to the tent just before the elder Mr. Biden gave a toast. The president’s brother James, who has pursued overseas business deals and is another target of the Republican-led House Oversight Committee, also sidestepped the cameras.

Ashley Biden, the president’s daughter, whizzed by in sequins, declining to answer questions about who had designed her dress. The Justice Department is investigating the theft by conservative operatives of a diary she kept while recovering from addiction.

Mr. Garland also avoided reporters. During the dinner, Mr. Garland stayed clear of the younger Mr. Biden, who circulated among the guests, stopping to laugh and talk with Bill Nelson, the former senator and current NASA administrator.

Perhaps no one illustrated the disconnect between a harmless few hours of partying and the partisan discord brewing outside than Nancy Pelosi, the former House speaker, who arrived with her husband, Paul. The 83-year-old Mr. Pelosi was attacked with a hammer last fall in their San Francisco home by a man who espoused far-right conspiracy theories. Mr. Pelosi, who had been wearing hats in public for months, this time showed off his gray hair and said he was feeling “great.”

In this crowd, the pace of footsteps seemed to correlate directly with each invitee’s relative interest in speaking with reporters. Representative Ro Khanna, Democrat of California and one of the lawmakers who had requested that Mr. Modi deliver an address to Congress earlier in the day, slowed to answer a question about whether he was satisfied with the prime minister’s remarks on human rights: “I thought it was very good that he talked about celebrating all faiths,” Mr. Khanna said before heading out to the tent.

Unlike previous dinners, the event was low on celebrity wattage, but several influential Indian and Indian American figures made the cut, including Indra Nooyi, the former chief executive of Pepsi; Mukesh Ambani, the billionaire and philanthropist; and Vimal Kapur, the chief executive of Honeywell.

Otherwise, the guest list appeared to prioritize political allies, a few provocative adversaries, and deep-pocketed donors as Mr. Biden’s campaign for re-election gears up. Tim Cook of Apple attended, as did John Morgan, a Florida-based donor. James Murdoch, the son of Rupert Murdoch, also attended. The younger Mr. Murdoch hosted a fundraiser for Mr. Biden last October.

Joshua Bell, the violinist who was set to perform during the dinner, was asked what he thought of Mr. Modi. “I try to stay away from politics, but I love Indian music,” he said, before a military aide pulled him inside.

By the end of the dinner, the prime minister was one of the few guests who had publicly waded into politics.

“You are soft-spoken,” Mr. Modi told the president, “but when it comes to action, you are very strong”

Doug Mills contributed reporting.