Theresa May, the leader of the UK’s Conservative Party and its embattled prime minister, is only the second woman to hold either roles. On June 8, following a series of campaign missteps and a late surge from Labour Party rival Jeremy Corbyn, her party lost its majority in parliament in the UK’s snap election. May has vowed to stay on as prime minster despite growing pressure to resign.

May, who in 2005 founded Women2Win, an organization within the Conservative Party to promote female representation in office, considers herself a feminist (and has a t-shirt to prove it). She has also expressed her awareness that the quality of her work as a politician matters for gender equality. “When I read it and hear it, what I feel is responsibility,” she said in 2012 about being called the most powerful woman in UK politics. “There’s an added reason for me to try to do my best—to show that a woman in this position can do my job.”

And yet, feminists have not universally embraced May as one of their own. Are they, as many conservatives seem to believe, using identity affirmation disingenuously to promote liberal politics while excluding those with different partisan leanings?

After all, Sarah Palin was not exactly held up as a paragon of women’s empowerment during her vice-presidential campaign. Before Palin, Phyllis Schlafly was a prominent leader in the Republican Party, and had a key role in moving it to the right. Both of the UK’s female prime ministers have been conservative, and so is—though it’s a bit difficult to equate American and European politics—Angela Merkel. Not to mention the impressive political longevity of Marine Le Pen, the driver of the French far-right’s ascent.

The question of what makes a powerful woman empowering to other women is a complex one that intersects with contemporary political mores and the fight for women’s representation. On the one hand, having more women—of any political belief—in positions of power is a pre-condition of female empowerment, and should be celebrated as such. But there is also an argument to be made that conservative women in power do not change the structure of power, too often subscribing to male-centered views of the world, and therefore do not contribute to institutional gender equality on a broad scale.

Many liberal women consider their gender identity a fundamental element that informs their political choices, explains Charlotte Walker-Said, a professor of history at CUNY’s John Jay College. Meanwhile, conservatives “want to be seen, and see themselves, as principled voters, instead of allies for women.” This often leads to a conservative rejection of the idea that gender should influence political choices. (Feminists would counter that their fight for women’s equality is the reason conservative women have any access to power at all.)

That right-wing political rhetoric doesn’t mesh perfectly with the ideals of the female empowerment movement has always been a part of radical feminist discourse. In her 1983 book Right-Wing Women, Andrea Dworkin argues that some women may prefer conservative politics because maintaining the patriarchal hierarchy feels safe.

“There are two aspects to any serious critique of male dominance: that women have been excluded from male forms of power, and that power has been defined on male terms,” Catharine MacKinnon, a professor of law at the University of Michigan and long-term visitor atat Harvard Law School who authored several books on feminism, tells Quartz. Conservative women may get access to power, but that won’t necessarily change the nature of the power itself—especially if conservative women actively promote traditional gender roles on their path to political success.

But it’s not only conservative women who choose not to wield their power wisely, according to MacKinnon: Liberal women, too, sometimes fail to challenge a masculine view of power. These people, she says, shouldn’t be viewed as particularly empowering, either. “Whether a woman in a male-defined position of power is empowering to women is not a matter of whether she is liberal or conservative,” MacKinnon explains, “but whether she uses the power of her position to advance women other than herself.”

The question then, seems to be whether it’s possible to thoughtfully critique women without diminishing their overall role in history and holding them to higher standard than men. Why can’t feminists acknowledge the importance of Margaret Thatcher as a shrewd politician and powerful woman, despite her politics?

The reason is an unresolved—and perhaps unsolvable—tension between individualistic and incremental progress for women (the tiny cracks in the glass ceilings, if you will). Feminists firmly believe that sweeping institutional change can only be achieved if the women in power implement women-friendly policies that eventually change society’s dynamics.

“The important thing, I think, is for feminists not to conflate women with feminism, because really what feminists want is more feminist women in power,” Ronnee Schreiber, a professor of political sciences at San Diego University and author of Righting Feminism, tells Quartz.

This is a difficult position to hold. Though the mainstream understanding of feminism often defines equality as its goal, radical feminist theory holds that it isn’t enough for women to seek individual promotion, they must also uplift their fellow women. Pop feminism is not always as clear on this second goal, in part because feminists can be wary of being asked “to judge or criticize women or say someone else is not feminist.”

However, Schreiber notes that there has always been “a strand of feminism that’s been very much just about individualistic women’s empowerment,” and that this attitude may be becoming prominent now as more women—who may or may not share radical feminist views—get to important roles in society.

Ultimately, it would be fair to acknowledge the progress, though incremental, that comes when women climb the political or corporate ladder. “Even if we are frightened by Le Pen, for example,” Schreiber says, “the fact that women can achieve those standards is obviously one minor sign of progress.”

But it is fair, too, fair to draw a distinction between powerful women who believe achieving personal influence is symbolism enough, and powerful women who make it their goal to fight for institutional change, and the promotion of all women.