Republicans, championing individualism, are philosophically wary of allying themselves with identity groups as Democrats have done — even if critics charge they have sent coded messages to groups such as Southern whites and the white working class.

“I guess I would say I’m not someone who thinks in terms of gender,” said Sharon Fraser Toborg, 48. She is raising four children in Barre, Vt., and resents that her choice to stay home despite Ivy League and graduate degrees still draws condescension from many women. She did not back Mr. Trump in the primaries, but preferred him in the end to Mrs. Clinton. “I’m someone who thinks in terms of capabilities, so to me how many men or women are in a particular president’s cabinet, I don’t keep score. I don’t believe only women can understand so-called women’s issues.”

That unease with gender as a unifier exists for those on the right who support Mr. Trump and those who declared themselves Never Trump.

Kori Schake, a research fellow at the Hoover Institution who served on the National Security Council under President George W. Bush, joined a group of Republican national security officials in a public letter pledging not to vote for him.

“If you are going to make a sweeping claim of gender opposition to the president, you have to account for those women who voted for him and continue to support him,” she said. “It seems to me a better broader argument to make against the president is to join forces across gender lines, across all manner of lines, and argue for the respect of human dignity.”

For years, conservative women have wrestled with the very idea of feminism. Many refused the label because they saw it as tarnished by association with the left, even as they pursued careers or won prominence in public life.

“Conservative women say ‘don’t put me in the feminism bloc’ because somehow it’s emblematic of a whole set of liberal issues that may have nothing to do with promoting women,” Mrs. Mitchell said.