LAS VEGAS — Pete Buttigieg, the mayor of South Bend, Ind., on Saturday directly confronted one of his biggest vulnerabilities as a contender for the Democratic presidential nomination: running as a white man who has led a life of relative privilege at a time when many in his party are eager for a woman or a minority candidate to become their next leader.

Speaking at a fund-raiser for lesbian, gay, bisexual and transgender causes, Mr. Buttigieg drew on his own experiences as a gay man in a predominantly straight society. But he also rejected the idea that “there are equivalencies” in the forms of discrimination experienced by different minority groups and individuals.

“I may be part of the L.G.B.T.Q. community. But being a gay man doesn’t even tell me what it’s like to be a trans woman of color in that same community, let alone an undocumented mother of four or a disabled veteran or a displaced autoworker,” he said at the event, hosted by the Human Rights Campaign.

Mr. Buttigieg recalled the experiences of several historically oppressed groups and the political movements that brought greater social and political equality, including Latino farm laborers, black civil rights activists and the modern gay rights movement that grew out of the Stonewall rebellion in Greenwich Village. He called for “the beginning of a new form of American solidarity” among people who understand that they live “in a society that sees us for what makes us all different.”