In 2009, Raymond Buckley was the only openly gay state chairman in the Democratic Party. His state, New Hampshire, was one of very few that had passed a law making same-sex marriages legal. Barack Obama, the new president, held a position that was then the norm for Democratic politicians: that marriage should be reserved for heterosexuals. Ten years later, being openly gay or lesbian and in politics is hardly out of the ordinary, though it is far more common among Democrats than Republicans. Mr. Buckley was one of two gay men, in fact, who ran for national party chairman in 2017. The other was Pete Buttigieg, the mayor of South Bend, Ind. Mr. Buttigieg’s campaign for president, which he made official this month, underscores how much easier it is for gay, lesbian, bisexual and transgender people to hold public office today.