Liberals envisioned a multiracial coalition. Voters of color had other ideas.

The state political and cultural establishment worked as one to pass this ballot measure. The governor, a senator, members of Congress, university presidents and civil rights leaders called it a righting of old wrongs.

“Women and people of color are still at a sharp disadvantage by almost every measure,” The Los Angeles Times wrote in an editorial endorsement.

Yet on Election Day, the proposition failed by a wide margin, 57 percent to 43 percent, and Latino and Asian-American voters played a key role in defeating it. The outcome captured the gap between the vision laid out by the liberal establishment in California, which has long imagined the creation of a multiracial, multiethnic coalition that would embrace progressive causes, and the sentiments of many Black, Latino, Asian and Arab voters.

Variations of this puzzle could be found in surprising corners of the nation on Election Day, as slices of ethnic and racial constituencies peeled off and cut against Democratic expectations.

“We should not think of demography as destiny,” said Professor Omar Wasow, who studies politics and voting patterns at Princeton University. “These groups are far more heterogeneous than a monolith and campaigns often end up building their own idiosyncratic coalition.”

Asian-American Californians opposed the affirmative action measure in large numbers. A striking number of East and South Asian students have gained admission to elite state universities, and their families spoke to reporters of their fear that their children would suffer if merit in college selection was given less weight. That battle carried echoes of another that raged the past few years in New York City, where a white liberal mayor’s efforts to increase the number of Black and Latino students in selective high schools angered working- and middle-class South and East Asian families whose children have gained admission to the schools in large numbers.

“There’s more texture to California blue politics than you might think,” said Lanhee Chen, a fellow at the conservative Hoover Institution at Stanford University and policy director for Mitt Romney’s 2012 presidential run. “Identity politics only go so far. There is a sense on affirmative action that people resent being categorized by progressives.”

Latinos, too, appear sharply divided. Prominent Latino nonprofit and civil rights organizations endorsed the affirmative action proposition even as all 14 of California’s majority-Latino counties voted it down.

Latinos make up more than half of San Bernardino County’s population, although significantly fewer turn out to vote. More residents there voted on the affirmative action proposition than for president, rejecting it by a margin of 28 percentage points. In rural Imperial County, in the southeastern corner of the state, 85 percent of the population is Latino. The voters there who gave Joseph R. Biden Jr. a nearly 27-point margin of victory went against the affirmative action measure by 16 percentage points.

The results suggest that Democrats may need to adjust their strategy as the complexities of class, generation and experience, and the competing desires of these demographic groups become clear. Since the dawn of the 21st century, it has become commonplace for party leaders to talk of a rising demographic tide that is destined to lift the Democrats to dominance. That liberal coalition is seen as resting on a bedrock of upper-middle-class white voters, alongside working- and middle-class Black, Latino and Asian voters.

In broad strokes, that narrative held. Black voters, along with a shift in the white suburban vote, played a pivotal role in delivering Georgia to the Democratic column (although so closely that a statewide audit is taking place). So, too, Black voters in Pittsburgh and Philadelphia voted overwhelmingly for Democrats — as did well-to-do majority-white suburbs — and gave Pennsylvania and therefore the national election to President-elect Biden.

In Arizona, Latino voters piled up large margins for Mr. Biden and tipped the state narrowly into the Democratic column for the first time since 1996. Representative Ruben Gallego, the Democratic congressman from Phoenix who is a former Marine and a Harvard graduate, noted that several decades of aggressive tactics by Republican governors and white sheriffs had stirred activism among the young Latinos who dominate politics there.

“The Republicans caught Latino lightning in the bottle in Florida and South Texas, but not here,” Mr. Gallego said. “We are very politicized. It’s just important that white liberals don’t impose their thoughts and policies on us.”

Aside from those successes, however, the election presented complications wrapped one inside another for Democrats. In Texas and Florida, in California and in Colorado (where New York Times exit polls found that roughly 40 percent of white voters and 38 percent of Latino voters cast ballots for President Trump), the assumption that people of color would vote as a liberal Democratic bloc often proved illusory.

John Judis is a liberal writer and scholar who in 2002 co-wrote “The Emerging Democratic Majority,” which became a seminal text for those who saw the Democratic Party as a political tide rising. He has since backed off that a touch.

“‘People of color’ is a term that’s been adopted by the cultural left as a way of arguing that if these groups proportionately voted Democratic in the past, they will do so in the future,” Mr. Judis said. “I don’t see how you can make the argument.”

Viewing the Latino vote as monolithic fails, of course, to capture the often sharply varying politics and ethnicities of people hailing from nearly two dozen countries on two continents. The same is true when examining the behavior of Asian-American voters.

Philadelphia offers a snapshot: A record number of Latinos in the city, which is heavily Puerto Rican and Dominican, turned out and buoyed Mr. Biden. Yet exit polls also found that Latino voter support there for Mr. Trump leapt to 35 percent this year from 22 percent in 2016. In Milwaukee, an analysis by Urban Milwaukee reported an uptick in the Latino working-class vote for Mr. Trump, although a majority still favored Mr. Biden.

Along the Rio Grande in Texas, where some Mexican-American families, known as Tejanos, have roots that extend back four centuries, the vote margins shifted dramatically in 2020. Latino turnout soared, almost entirely to the benefit of Mr. Trump. Although Mr. Biden obtained more total votes in the four counties of the Rio Grande Valley than Hillary Clinton did in 2016, his margins of victory fell sharply.

The reasons offered for these results include poor field organizing by the Democratic Party, the cultural conservatism of some older Tejano families, and the fact that many in these often-dense counties find good-paying jobs with the Border Patrol.

Many voters, too, worried that Mr. Biden and the Democrats would impose a new coronavirus-driven shutdown, with dire consequences for the many thousands who own and labor for small businesses. Prof. Omar Valerio-Jimenez grew up in the Rio Grande Valley and teaches history at the University of Texas at San Antonio. Several of his old friends and cousins voted for Mr. Trump.

“They faced this challenge: Do they continue to open our stores and restaurants and churches, which lets us pay our bills,” he said, “or do we quarantine and not have the money to pay our bills?”

Muslim voters also confounded Democratic strategists with their support for Mr. Trump reaching 35 percent, according to The Associated Press. This, too, is a constituency difficult to pigeonhole, as it encompasses Africans, Arabs, South Asians and Europeans.

“A sizable number of Muslims have experienced Donald Trump and to the surprise of Democrats they said, ‘We want more of that,’” Shadi Hamid of the Brookings Institution said.

Analyzing vote shifts is a tricky business, particularly when trying to gauge why some Latino, Black or Arab voters moved from supporting a liberal Democratic candidate like Mrs. Clinton in 2016 to voting for a populist authoritarian Republican like Mr. Trump. Some analysts pointed to the appeal among male voters — regardless of color or ethnicity — of Mr. Trump’s masculine persona. Others mentioned the performance of the national economy, which had hummed along until the plague arrived.

There were small, intriguing changes in the Black vote as well. The Times’s exit polls in Georgia found that 16 percent of Black men voted for Mr. Trump. (Compared with 7 percent of Black women there.) And to chart the votes along the so-called Black Belt in Mississippi, which includes 10 counties along the Mississippi River, was to find that although Mr. Biden won handily, his margin in nearly every county was two to three percentage points smaller than Mrs. Clinton’s.

The unanswered question is whether the 2020 election will be a one-off, the voting patterns scrambled by an unusually polarizing president who attracted and repelled in near equal measure. If it signals something larger, political scientists noted, some Latino and Asian voters might begin to behave like white voters, who have cleaved along class lines, with more affluent residents in urban areas voting Democratic while a decided majority of rural and exurban residents support Republicans.

Then there is California, where the sands of change blow in varying directions. In 2018, Democrats swept the Orange County congressional seats. In 2020, the Republicans have rebounded and taken at least two of those seats.

The Republican candidate Michelle Steel, who is Korean-American, came out against the affirmative action proposition, a stance that proved popular with her Asian-American constituents, as well as many white voters. And on election night, Ms. Steel rode that support to a narrow win against the incumbent Democratic congressman, Harley Rouda.

“This is the challenge for liberal Democrats,” Professor Wasow said. “In a diverse society, how do you enact politics that may advance racial equality without reinforcing racial divisions that are counterproductive and hurt you politically?”