NEW YORK — A sizable number of U.S. voters say they’d have some hesitancy about supporting an LGBT candidate for president, according to a new poll from The Associated Press-NORC Center for Public Affairs Research. In fact it’s an issue for many more than a candidate’s race or gender.

In the poll, 32 percent of registered voters said they would be less excited about supporting a presidential candidate who was gay, lesbian or bisexual; 42 percent said that about a transgender candidate. By contrast, only about 1 in 10 voters expressed such hesitance in regard to a candidate’s gender or race.

Yet many LGBT candidates have overcome such attitudes, even winning statewide elections, and political experts predict that the path for future LGBT office-seekers will steadily grow smoother.

One intriguing test case: the presidential campaign of Pete Buttigieg, the mayor of South Bend, Indiana, who has gained significant support with minimal controversy over the fact that he’s gay.

“While the polling data shows there is still reluctance to vote for an LGBT candidate among a minority of the electorate, that reluctance has been steadily declining,” said Professor Charles Franklin, a pollster at Marquette University in Milwaukee. “There are more success stories demonstrating that LGBT candidates can win despite this disadvantage.”

He cited two LGBT candidates who won statewide races in swing states last year: Democrats Tammy Baldwin of Wisconsin, easily re-elected to the U.S. Senate, and Jared Polis of Colorado, the first openly gay man elected governor.