Who gets to define what it means to be pro-women? The left has staked its claim. The public face of resistance to President Trump began with a “women’s march.” An estimated three to five million turned out worldwide, brandishing signs like “Women’s Rights Are Not Up for Grabs” to deliver the message that to be a woman was to be against this president.

Now the same groups that organized the march are proposing a general strike — “a day without a woman” — to show that women continue to oppose him and that the world would be lost without them.

The leaders of these protests argue that women’s causes — abortion, contraception, economic equality, immigration, criminal justice — essentially demand liberal solutions.

That leaves conservative women — those who support the president and those who don’t — out. Their opponents claim to represent the best interests of an entire gender, one that happens to be theirs.

Cleta Mitchell, a partner at the law firm Foley & Lardner who has long been active in conservative politics, finds nothing but hypocrisy on the part of women who claim to speak on her behalf.

“This women’s march, I kept thinking, so what are we? Chopped liver?” she said. “We’re invisible when it comes to talking about women. These women don’t represent me or anyone I know. I don’t think it’s fair to say his comments hurt the Republican Party image any more than Bill Clinton’s behavior tarnished the Democratic Party.”

The early days of the Trump administration have provided ammunition to Democrats who have long tried to brand Republicans as anti-women. Mr. Trump immediately reinstated the “gag rule” denying federal funds to overseas organizations that include abortion as part of family planning services. His cabinet has the highest number of white men since Ronald Reagan’s. And the now infamous silencing of Elizabeth Warren coined a new rallying cry: “She Persisted.”

Mary Matalin, the veteran Republican strategist who switched her party affiliation to Libertarian last spring, believes any attempt to brand the Republican Party as anti-women will fail. Hillary Clinton’s repeated attacks on Mr. Trump’s misogyny did not sway independents and moderate Republicans to reject him, for example. Of women who voted for him, 78 percent said they were bothered to some extent by his treatment of women.

“The critical fallacy in the liberal logic of identity politics is that — demonstrably — ‘groups’ don’t think homogeneously; they don’t behave homogeneously,” Ms. Matalin wrote in an email.

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.

Lani Candelora, 39, wrote to The Times in response to a question about who was, or was not, attending the marches. “It might be a shock to The New York Times, but many American women are feeling hope and joy in the change of administration,” she wrote. “We believe our families will have financial relief, that we’ll have a better chance of everyone finding gainful employment, that we’ll have affordable health insurance again for our families, that our religion will no longer be shunned and persecuted by the presidential administration, that the phony selfish feminism promoted by this women’s march is not continuously projected onto millions of other women who strongly disagree.”

Yet for some conservative women — a minority, election results show — Mr. Trump’s behavior was a breaking point.

Marybeth Glenn, 29, a Wisconsin-based blogger who said she is committed to fiscal conservatism, gun rights and opposition to abortion, denounced Republican men for standing by Mr. Trump in a tweet storm that went viral before the election. As a result, she said, she was subjected to insults and threats by Trump supporters.

“I didn’t see men on the right standing up to men like that,” she said. “That was a wake-up call for me. I think women should be taking away the message from the Republican Party that they’re not going to stand with women.”

She now considers herself an independent and does not rule out voting Democratic in the next election. “I hope they reach back and speak to us as well,” she said. “A lot of us are politically homeless right now.”

Abortion is, for many, a key sticking point, dividing women who might otherwise find common ground. There are issues that have unified women across the aisle — sex trafficking is one; some aspects of criminal justice have the potential to be another.

Sabrina Schaeffer, executive director of the Independent Women’s Forum, which advocates conservative approaches to policies that affect women, said there is bipartisan concern that mass incarceration policies destroy families and communities. And Ms. Schaeffer, without directly mentioning his name, seemed to echo liberal women’s discomfort with this president when she said: “Most of us would like to see people in public office who speak well of women and who treat women well. Unfortunately, there are people are both sides of the aisle who don’t do that, and that’s a shame.”

The conservative vision of pro-women policies emphasizes free-market solutions and small government. That means the women’s forum opposes mandatory paid maternity leave — a policy Ivanka Trump pushed for during her father’s campaign — because it believes that will result in fewer jobs and lower take-home pay.

Mrs. Mitchell, like other conservatives, rejects what she sees as feminism’s emphasis on women as victims. “What is the right they don’t think we have?” she said. “I remember when we were fighting to change statutes, when women couldn’t serve on juries. It’s almost as if we are not allowed to claim victory.”