TAMPA, Fla. — Twenty years ago, Patrick J. Buchanan rocked the Republican convention in Houston by declaring there was a “cultural war” taking place for the soul of America, denouncing the Democratic Party as one that supported abortion, radical feminism and the “homosexual rights movement.”

“The agenda Clinton and Clinton would impose on America — abortion on demand, a litmus test for the Supreme Court, homosexual rights, discrimination against religious schools, women in combat — that’s change, all right,” said Mr. Buchanan, a conservative commentator who was a rival to President George Bush in the 1992 campaign. “But it is not the kind of change America wants.”

The speech — along with similarly sharp-edged addresses by the evangelist Pat Robertson and Marilyn Quayle, the wife of Vice President Dan Quayle — pushed issues like abortion, gay rights, religion and the role of women in society to the front of the stage, often loudly. Supporters of Mr. Bush pointed to the tone of the convention as one of the reasons he lost the election that November to Bill Clinton.

Yet Republicans gathered here to nominate Mitt Romney suggest that those speeches would hardly give them pause today. What many viewed as the fringes of the Republican Party 20 years ago have moved closer to the mainstream — evidence, Mr. Buchanan said, of the extent to which a Republican establishment that was once relatively moderate on social issues has been pushed rightward by grass-roots conservatives.