For most of the last two decades, Rep. Peter King represented a congressional district typical of Long Island: overwhelmingly white, solidly middle class and reliably Republican.

But last year, the contours of the 11-term Republican’s district shifted, leaving him in an area more representative of the changing face of the suburbs east of New York City: one-third minority, dotted with poverty and increasingly Democratic.

The demographics pose a political challenge—if not a threat—to Mr. King, a former chairman of the House Committee on Homeland Security, a go-to interview subject for CNN and Fox News and a conservative voice on immigration and terrorism issues.

“I’m not kidding myself,” Mr. King recently told a crowd of 150 of his new constituents at the public library in Brentwood, a Suffolk County community where the population is two-thirds Hispanic. “I know there’s many people here who didn’t vote for me, who won’t vote for me.”

Asked if the new politics of his district would affect his stances, Mr. King said, “You can’t be changing your views on important issues just depending on what your district is.”

In 2012, Mr. King went from representing a district that was 87% white, 7% Hispanic and 2% black to running in one that was 66% white, 20% Hispanic and 9% black, according to the state’s redistricting task force.

While Mr. King beat a Democratic political newcomer, Vivianne Falcone, with 60% of the vote last year, voter-registration numbers suggest he could face a serious challenge in the future.

The old district, situated mostly in Nassau County, was 40% Republican and 31% Democrat, according to state records. The new one, mostly in Suffolk County, is 35% Republican and 34% Democrat.

“Before the lines changed, no one even entertained the thought of challenging him,” said Ms. Falcone, a former teacher, who said she was considering running again. “He’s just not a good fit for this new district at all, and the only place where he had an abundance of supporters was his old district in Nassau County.”

Mr. King’s new district contains some of Long Island’s most diverse communities. Those include not just Brentwood but also Central Islip, Bay Shore and North Bay Shore, which are likely to lean Democratic, said Michael Dawidziak, a Long Island political consultant.

But it also includes Republican strongholds such as Massapequa—one of the few communities Mr. King retained in the redistricting—West Islip and Islip Terrace.

Mr. Dawidziak, who has worked with candidates of both parties, said Mr. King also benefited from name recognition and a reputation for blunt talk as he grapples with his new territory.

“He wouldn’t be Peter King if he wasn’t outspoken, and that’s part of his appeal,” Mr. Dawidziak said. “He’s always had that Reagan-esque appeal. People don’t feel they have to agree with him to like him.”

Richard Schaffer, chairman of the Suffolk County Democratic Committee, said Mr. King’s incumbency—and his “presence beyond his district”—gave him an edge over prospective challengers. Mr. Schaffer, who also serves as supervisor of the Town of Babylon, which is within Mr. King’s new district, also praised the congressman for his work after superstorm Sandy. “He’s paying attention to a lot of the things he should as a congressman. You know—the retail things.”

A forum last month in Brentwood was Mr. King’s first public meeting in that corner of his district. The gathering highlighted his outspokenness, as well as some of the incongruities between the congressman and his new constituents.

On some topics, the 69-year-old politician sought common ground. He emphasized his support of labor unions, and when asked by Tyzier King, 14, of Central Islip, about recent gang shootings, Mr. King said he wanted to expand background checks on gun buyers.

Mr. King—who introduced legislation in 1995 that would have made English the national language and closed bilingual education programs, and said he still supported such measures—had his words translated into Spanish by an interpreter.

And the congressman who roiled many Muslims two years ago by holding a hearing on Islamic radicalization found himself seated on stage next to a Muslim high-school student wearing a hijab. She was Samia Jabbar, 17, of Bay Shore, who represented a mosque in the district.

Mr. King also weighed in on the immigration-overhaul bill making its way through the Senate, saying he backed a path to citizenship for illegal immigrants as long as the legislation secures the borders.

Some immigrant advocates said they were surprised and encouraged by Mr. King’s view on the issue.

“He showed that he’s open to comprehensive immigration reform, and that he wants to interact with the new community that he represents,” said María Magdalena Hernández, 48 years old, of Bay Shore, who asked Mr. King about his stance on the bill.

The Islip Town branch of the NAACP and the Long Island Civic Engagement Table, an immigrant advocacy group [including Make the Road New York], organized the forum as a way to introduce Mr. King to minority communities.

But the congressman also displayed his signature willingness to risk political incorrectness.

When Samia Jabbar, 17, of Bay Shore, daughter of a local imam, said she feared Mr. King’s rhetoric about Islamic radicalization could lead to discrimination against Muslims, Mr. King defended his views.

“I’ll be very honest with you: The fact is we do face a threat today which comes from the tiny percentage of the Muslim community, of Islamic terrorism,” he said. “That is the greatest threat facing our country today and it comes from within the Muslim community.”

Afterward, Ms. Jabbar said she looked forward to coming to a mutual understanding with Mr. King. “He seems like a good guy,” she said. “It’s just like the one thing that we’re clashing on is important to us. It feels like we’re still waiting for him to work with us, you know?”

Astrid Fidelia, president of the Haitian-American Political Action Committee of New York, said she was disappointed Mr. King didn’t support increasing the federal minimum wage at this time, but was happy he visited. “This is a beginning,” she said, “and I thought it was good that he took the time to be here, to meet everyone.”

Others there were less diplomatic. “It took him all this time to get here,” said Amparo Sadler, 59, of Central Islip. “I don’t really feel like he’s here for anything. He’s trying to get the minority vote.”

After staying to shake hands and pose for photographs, Mr. King said he had no illusions about how the attendees were likely to vote, and said winning some over would require changing some of the hard-edged image he had developed.

“I don’t know if it changed anybody’s vote, but it can certainly make for a more harmonious district,” he said. “I’m here to say, as long as they know I’ll work for them and they can trust me and I can trust them, then great.”

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