WASHINGTON » Tuesday’s presidential election results showed the American voting public has not only become more permanently diverse in its makeup, but also in its mindset.

Obama bet, and won, on the assumption that the electorate would retain much of the age, ethnic and racial diversity he brought out in 2008. But across the country, voters affirmed changes in social policy that show a culture changing along with it.

The trend is troublesome for Republicans, who nominated in Mitt Romney a candidate who was more socially moderate than his rivals for the GOP nod and who tried in the campaign’s closing days to reach out to the broader electorate.

“The country is changing and the people our party appeals to is a static group,” GOP strategist Mike Murphy said.

Younger voters and minorities came to the polls at levels not far off from the historic coalition Obama assembled in 2008.

Voters also altered the course of U.S. social policy, voting in Maine and Maryland to approve same-sex marriage, while Washington state and Colorado voted to legalize recreational use of marijuana.

In the heartland, where the conservative Christian tradition still runs deep, Minnesota voters defeated a proposed constitutional amendment to ban gay marriage. In Iowa, where opponents of gay marriage ousted three state Supreme Court justices two years ago, a fourth judge beat back a similar attempt Tuesday and Republicans intent on pursuing a constitutional ban failed to gain the single seat they needed.

On social issues, exit polls conducted Tuesday for The Associated Press found a public more apt to take the liberal position. For example, roughly 60 percent of voters said abortion should be legal in all or most cases, the highest share since the mid-1990s.

The reality caught off guard Republicans, who banked on an electorate more monolithic and more conservative than four years ago. And it foreshadowed changes over the next generation that could put long-held Republican states onto the political battleground maps of the future.

“Clearly, when you look at African-American and Latino voters, they went overwhelmingly for the president,” said John Stineman, a Republican strategist from Iowa. “And that’s certainly a gap that’s going to require a lot of attention from Republicans.”

The exit polls showed that voters mirrored the makeup of the electorate four years ago, when Obama shattered minority voting barriers and drove young voters to the polls unlike any candidate in generations.

White voters made up 72 percent of the electorate — less than four years ago — while black voters remained at 13 percent and Hispanics increased from 9 percent to 10 percent.

That flew in the face of GOP assumptions that the fierce economic headwinds of the past three years and the passing of the novelty of the first African-American president would trim Obama’s support from black voters, perhaps enough to make the difference in a close election.

However, Obama carried Virginia, the heart of the Old South, in part by having increased his record support from black voters there in 2008, which reached 18 percent, to more than 20 percent, according to Obama campaign internal tracking polls.

It was also reflected in turnout that matched his 2008 totals in places like Cleveland, which helped Obama carry Ohio solidly despite Romney’s all-out effort there in the campaign’s final weeks.

“Republicans have been saying for months” that Obama’s black support would slip, Democratic pollster Paul Maslin said. “And what happens? When African-Americans had the chance to affirm him, they came out in droves.”

Obama won in 2008 by carrying several long-held Republican states, including North Carolina, Virginia and Indiana. And while Romney easily carried Indiana and narrowly peeled back North Carolina, the fact that Obama held Virginia points to a long-term demographic shift that survived the pressures of the poor economy.

Obama carried every contested state except North Carolina by aggressively registering first-time voters. He matched his share of the youth vote from 2008, and nearly matched his support from seniors.

In a sign these changes are more glacial than seismic, Obama, who announced his support for gay marriage in May, lost North Carolina, where voters there overwhelmingly voted against allowing gay marriage the same month.

There also were signs divisions between opponents had deepened.

Voters were more ideologically polarized than in 2008 or 2004. The share of moderates dipped slightly to 41 percent, while 25 percent called themselves liberal, the highest share saying so in recent surveys of voters as they leave their polling places. Thirty-five percent called themselves conservative, about the same as the previous two presidential contests.

The 2012 electorate mirrored 2008 in terms of party identification and racial makeup, with self-identified Democrats topping Republicans and independents.

During his victory speech, Obama nodded to the Democratic coalition he had held together.

“It doesn’t matter if you’re black or white, or Hispanic or Asian, or Native American, or young or old or rich or poor, able, disabled, gay or straight,” Obama told his crowd of supporters gathered in Chicago. “You can make it here in America if you’re willing to try.”

Assumptions by Romney about the minority and youth turnout weren’t the only ones that turned out to be wrong.

While voters considered the economy the driving issue in the election, they did not hold Obama wholly responsible, as Romney long had assumed they would.

That realization forced Romney to pivot late in the campaign and attempt to turn the election into a choice of competing visions. Republicans argued late in the campaign that Romney’s performance during the first of three debates had energized a groundswell of enthusiasm seen in their polling.

But it seemed Obama’s support was quietly amassing with more vigor, GOP strategists said.

“There really wasn’t an enthusiasm gap,” said Republican strategist Charlie Black, an informal Romney adviser. “And independents didn’t break our way.”