Suresh Reddy, a centrist Democrat and city councilman, is watching the Republican presidential primary with a mix of pride and disappointment.

When Mr. Reddy and his wife, Chandra Gangareddy, immigrants from southern India, settled in the Des Moines suburbs in September 2004, they could count the number of Indian American families on one hand. Only one Indian American had ever served in Congress at the time, and none had dared to mount a bid for the White House.

Now, for the first time in the nation’s history, two Indian Americans — Nikki Haley and Vivek Ramaswamy — are serious presidential contenders who regularly invoke their parents’ immigrant roots. But their deeply conservative views, on display as they seek the Republican nomination, make it difficult for Mr. Reddy to fully celebrate the moment, he said.

“I’m really proud,” he said. “I just wish they had a better message.”

That disconnect, reflected in interviews with two dozen Indian American voters, donors and elected officials from across the political spectrum — in the early voting states of Iowa, New Hampshire and South Carolina and across the country — may complicate the G.O.P.’s efforts to appeal to the small but influential Indian American electorate.

Indian Americans now make up about 2.1 million, or roughly 16 percent, of the estimated 13.4 million Asian Americans who are eligible to vote, the third largest population of Asian origin behind Chinese and Filipino Americans, according to a Pew Research Center analysis of the 2021 American Community Survey. Indian Americans also have tended to lean more Democratic than any other Asian American subgroups, according to Pew.

Though a small slice of the overall electorate, the demographic has become one of the fastest-growing constituencies, and is large enough to make a difference at the margins in swing states and in purple suburbs, including in Florida, Pennsylvania, Michigan and Nevada.

Debate over the prominence of Ms. Haley and Mr. Ramaswamy is playing out in Indian American homes and places of worship in Des Moines and beyond. In interviews, many described their rise as a political triumph at a time when Indian Americans have become more visible in fields beyond medicine, tech and engineering.

Venu Rao, a Democrat and retired engineer and program manager in Hollis, N.H., said Ms. Haley and Mr. Ramaswamy captured the ideological diversity among South Asian Americans, even if he doesn’t agree with their positions.

“I am glad that we have a choice,” Mr. Rao said.

But many of those interviewed also expressed frustration and dismay over the candidates’ hard-line positions on issues like race, identity and immigration. Some worried Mr. Ramaswamy’s pledges to dismantle agencies like the Education Department would destroy the same institutions that had been crucial to Indian American success and upward mobility.

Others said they appreciated Ms. Haley’s attempts to strike a more center-right tone on some topics like abortion and climate change but indicated concern about what they described as her tepid pushback against former President Donald J. Trump and his 2020 election lies.

“It can be really easy to see this as a win and be like, ‘Oh my god — look there, those are two brown faces on national TV. That’s amazing,’” said Nikhil Vootkur, 20, a student at Tufts University in Boston. But, “the diaspora, it has matured, and when a diaspora matures, you have a lot of ideological cleavages.”

Over the past decade, Indian Americans have been rapidly climbing the political ranks. Vice President Kamala Harris, a Democrat and the daughter of an Indian mother and Jamaican father, is the first woman, first Black person and the first Asian American to hold her office.

In 2015, Gov. Bobby Jindal of Louisiana, a onetime rising Republican star, became the first Indian American to run for president. But Mr. Jindal, who changed his name, Piyush, to Bobby and converted to Christianity when he was young, made a push for assimilation that turned off many Indian American voters. Ms. Haley and Mr. Ramaswamy have toggled between proud embraces of their roots and scorching criticism of the “identity politics” that has been known to alienate the Republican Party’s largely white and evangelical Christian base.

Mr. Ramaswamy, 38, a political newcomer and millionaire entrepreneur from Cincinnati, Ohio, uses his Hindu faith to connect with Christian voters and expresses gratitude that his parents immigrated from the southwestern coast of India to the “greatest nation on Earth.”

Ms. Haley, 51, a former South Carolina governor and United Nations ambassador from Bamberg, S.C., has written and spoken extensively about her experience as the daughter of Sikh immigrants from northern India, including the pain of watching her father, who wears a turban, endure racism and discrimination.

Mr. Ramaswamy, who is running in the mold of Mr. Trump, has made a concerted effort to appeal to Indian Americans in the primary. He has made several appearances at the Hindu Temple and Cultural Center of Iowa, where many patrons have met his parents, and he has drawn the independent support of its Hindu priest, Khimanand Upreti, who in an interview described Mr. Ramaswamy as “very fresh and clean” and without Mr. Trump’s controversies.

On the trail, Ms. Haley has talked less about her identity and often describes her immigrant family in general terms. But in a response to a voter question at a town hall in Hampton, N.H., on Thursday night, she explained how her father’s experience with prejudice helped her connect with a hurting community and persuade state lawmakers to take down the Confederate battle flag at the South Carolina State House, after a white supremacist shot and killed nine Black parishioners in Charleston. She also used her parents’ immigrant background to tear into President Biden’s decision to provide temporary protected status and work permits for Venezuelan migrants.

“My mom would always say if you don’t follow the laws to get into this country, you won’t follow the laws when you are in this country,” she said.

At their home in Waukee, west of Des Moines, Nishant Kumar and Smita Nishant, who immigrated from New Delhi and Mumbai some two decades ago, and their daughter, Anika Yadav, 17, said the 2024 Iowa caucuses would be the first election they would all be able to participate in. The Nishants have only recently obtained citizenship, and Ms. Yadav will be old enough to vote in the next presidential election.

The family first became politically engaged when Barack Obama ran for president in 2008 — and would have backed Democrats in the past few elections if they could have voted. But as they weigh the 2024 presidential contenders, they have found Mr. Ramaswamy smart and refreshing, they said.

They have seen less of Ms. Haley, but Ms. Yadav says she likes Ms. Haley’s experience on foreign policy and the way she holds herself on the national stage, even if she has not made her Indian American identity central to her campaign.

“I think a lot of women, specifically young women, are leaning toward Nikki Haley — even young women who are Democrats,” she said.

Still, some Indian American Democratic-leaning voters and prominent Indian American Democrats expressed concern or sadness over Mr. Ramaswamy’s and Ms. Haley’s approaches to issues of race and identity, saying they fed into “model minority” stereotypes and carried dog whistles that minimized or diminished the specific systematic racism faced by Black Americans.

Both, when discussing their life story, tend to emphasize their successes as evidence of racial and ethnic progress in the United States. Both promote hard-line immigration measures and denounce race-conscious policies such as affirmative action in school admissions.

Mr. Ramaswamy in particular has generated criticism for suggesting white supremacy was an exaggerated “boogeyman” and for pledging to end birthright citizenship for the children of undocumented immigrants. Ms. Haley has said she opposes birthright citizenship for people who have illegally entered the country.

Representative Ro Khanna, a Democrat from California, criticized their approach on immigration and faulted them for ignoring the history of Asian exclusion in the nation’s immigration laws. The work of Indian and Black leaders during the civil rights movement helped open the pathways to migration and citizenship for Indian families to enter the United States, he said.

“Their story about the Indian American experience will not fully connect because it has so many omissions,” Mr. Khanna said.

But Bhavna Vasudeva, a longtime friend of Ms. Haley’s in Columbia, S.C., argued that Ms. Haley’s Republican values held real appeal for second-generation Indian Americans, adding that her approach to her family’s racial struggles exhibited a strong sense of “Chardi Kala,” an expression that for Punjabi and Sikh Indians and Indian Americans has become synonymous with “resilience” and a “positive attitude” in the face of fear or pain.

“You can’t tell anyone who is a brown woman about racism and discrimination,” Ms. Vasudeva, a donor to Ms. Haley’s campaign, said. “We have faced it all with our heads high and crown straight.”

Audio produced by Adrienne Hurst.