White men narrowly backed Hillary Clinton in her 2008 race for president, but they are resisting her candidacy this time around in major battleground states, rattling some Democrats about her general-election strategy.

While Mrs. Clinton swept the five major primaries on Tuesday, she lost white men in all of them, and by double-digit margins in Missouri, North Carolina and Ohio, exit polls showed — a sharp turnabout from 2008, when she won double-digit victories among white male voters in all three states.

She also performed poorly on Tuesday with independents, who have never been among her core supporters. But white men were, at least when Mrs. Clinton was running against a black opponent: She explicitly appealed to them in 2008, extolling the Second Amendment, mocking Barack Obama’s comment that working-class voters “cling to guns or religion” and even needling him at one point over his difficulties with “working, hard-working Americans, white Americans.”

She could not sound more different today, aggressively campaigning to toughen gun-control laws and especially courting black and Hispanic voters.