SAN DIEGO — The Republican Party keeps announcing its new modernity, declaring its new inclusiveness, swearing that it has changed and then showing that it hasn’t.

Witness Rand Paul, who is supposed to be one of its fresher, unconventional faces.

He spoke at a dinner here on Saturday, in a blazer and khakis instead of a suit, and once again presented himself as a Republican unusually in touch with the sensibilities of younger voters, especially concerned about the welfare of minorities and uniquely positioned to expand the party’s reach.

It was a refreshing pitch — until a medieval metaphor revealed an antiquated mind-set.

He was describing people’s need to feel that their personal information in cyberspace is as safe from indiscriminate government snooping as the documents in their dwellings have long been, and he mentioned the adage that “a man’s house is his castle.”Then he updated it: “Now we would say a man or a wife’s home is their castle.” A man or a wife’s?Aiming for a less sexist, more sensitive vocabulary, he came up with a more sexist, less sensitive one, casting women as auxiliaries of men.

This was no way to rebrand the party, no way to retire any image of it as a preserve for old white guys.

But it was emblematic. For all the party’s self-congratulation about a field of official and unofficial presidential candidates who depart from the fusty norm, the truth is that they don’t depart nearly enough.

Yes, they’re a racially diverse group, including Bobby Jindal, who is Indian-American; Marco Rubio and Ted Cruz, who are Cuban-American; and Ben Carson, who is African-American.

Yes, Rubio and Bush speak Spanish, as Bush did in Miami on Monday during his formal campaign announcement, which had the multiethnic flourish of a Coca-Cola Super Bowl commercial.

Yes, Cruz and Rubio are both under 45. Rubio in fact looks young enough to be Bernie Sanders’s grandson. He advertises an affinity for hip-hop and rap. He name-checks Pitbull and Nicki Minaj.

Paul, an ophthalmologist, highlights his travels to Central America to perform eye surgery on indigent Guatemalans. He cuts his own hair. And he urges criminal justice reforms, including lighter punishments for marijuana possession and use.

But he came across as more backward-acting than forward-looking during that strange sequence of interviews with female journalists a few months ago, when he admonished and interrupted them.

And his Republican rivals, beneath their playlists and campaign choreography, aren’t so impressively in touch with the times either.

Although more than 70 percent of American adults under 35 support same-sex marriage, not one candidate in the sprawling Republican field has explicitly taken that position, and most have expressed impassioned opposition.

Although an increasing fraction of American adults, including about a third of those under 35, now pronounce themselves religiously unaffiliated, there’s no sense of that drift in the emphatic religious testimonials of most of the Republican candidates, including Bush, Rubio and Scott Walker, who introduces himself as a preacher’s son.

Almost all of them are at odds with young Americans’ belief in climate change and stated desire for immigration reform.

And none of the leading contenders has a pitch that strongly reflects a recent Gallup poll’s finding that more Americans label themselves socially liberal than at any point in the last 16 years. These Americans finally match the percentage of those who call themselves socially conservative.

Where’s the Republican presidential contender for them?Where’s the Republican candidate who can enter into an important, necessary debate about the size, role and efficacy of government without being weighed down by a set of statements and positions on social issues that seem tailored to placate the religious right and to survive the primaries, not to capture voters in the center? You’re not allowed to say George Pataki unless he reaches 5 percent in the polls. Last I checked, he’s about four points shy of that.

Yet again there’s a void, and Hillary Clinton and her advisers have certainly noticed it. That awareness informed her own speech on Saturday, on Roosevelt Island, where she made many references to young Americans, to L.G.B.T. Americans, to minorities, to working women. Her remarks constituted a road map of the precise terrain that Democrats want to keep — or put — beyond Republicans’ reach.

And she sought to counteract the familiarity of her presence with the novelty of her promise. She pictured a woman in the Oval Office.

On the other side of the country, Paul pictured a woman in a castle . and all he saw was a wife. The ophthalmologist needs better vision. So does his party, if it wants passage across the moat to the White House.