When Sister Donna Markham, OP, assumes leadership of Catholic Charities USA later this year, three of the Catholic Church’s largest social service groups in the United States — Catholic Charities, Catholic Relief Services, and the Catholic Health Association — will be led by women, a paradox, some say, in a Church that restricts women from the priesthood, and thus from ascending to the highest levels of institutional power.

“When it comes to the Catholic Church and women, it is really interesting because you have the very visible and hard line: women cannot be priests. Therefore women, by virtue of being women, cannot occupy the positions of power,” said Kathleen Sprows Cummings, director of the Cushwa Center for the Study of American Catholicism at the University of Notre Dame.

But women have historically held positions of great leadership in the Church regardless, she said, usually through religious communities that saw women leading universities, hospitals, and even Catholic newspapers, long before their secular sisters were able to take advantage of similar opportunities.

Carolyn Woo, president of Catholic Relief Services and the former dean of the business school at Notre Dame, said the Church has many female leaders, but doesn’t do a great job of making them visible.

Woo, who leads 5,000 employees working in 93 countries on anti-poverty programs with a budget of more than $600 million, said that the shared experience of faith in the Catholic sector helps women bridge the gender divide that exists in some other fields. (“I don’t golf and I’m not into sports,” she said, laughing.) But she acknowledged that there still are cultural issues women confront in the Church.

“It’s not unusual today, when going to meetings and functions, sometimes people will only acknowledge your male colleagues, and you almost become invisible,” she said.

Woo came to the United States from China as a student 40 years ago, and said she’s always had to navigate as an “outsider,” first as an immigrant, then as a woman in business.

She recalled being shocked when, during a lesson on investment tools, none of her female students projected that they would become CEOs, while many of the male students did. Then she realized she had not imagined that for herself, either.

“It’s not just that men hold certain points of view, because some women do, too,” she said, noting that it’s a topic fraught with many considerations. “There are many choices in life that are very noble, and being CEO is not the only metric one should measure one’s worth by.”

Sister Carol Keehan, DC, leads the Catholic Health Association, a membership organization representing more than 2,000 Catholic hospitals, long-term care facilities, and other health care entities.

Sister Keehan, dubbed “the most powerful person in healthcare” in 2007 by Modern Healthcare magazine, said that Pope Francis himself has called for more women in positions of leadership, and hopes the fact that it’s happening in the United States could inspire the Church in other countries.

“To be able to say, look at what women have done for these organizations, is a really important thing to point to when people say, oh no, women can’t do it, or there’s not a role for them,” she said.

Sister Keehan is in Haiti with Woo to dedicate a 200-bed, $22 million hospital today, a project that was funded by the hospital association and relief organization after the devastating earthquake there in 2010.

Polls find that most Catholics in the United States are at odds with their Church when it comes to the role of women.

A 2009 Pew study found that of 39 percent of young adults who leave the Catholic Church, and who are now unaffiliated with a religion, said they were “unhappy with the way religion treated women.”

In a separate study last year, nearly 70 percent of US Catholics said they believe women should be ordained to the priesthood.

Of course, such a shift is unlikely.

Pope St. John Paul II declared the matter settled, saying that it is impossible for the Church to open the priesthood to women, and Pope Francis seems to agree.

Some Catholics, however, don’t see the prohibition on ordination as preventing women from exercising leadership.

“You don’t a need collar to make a difference in the Church,” said Kim Daniels, former spokeswoman for the president of the US Conference of Catholic Bishops and now a senior adviser to Catholic Voices USA. “The Church, as Pope Francis has said, is clear on where it stands on women priests. At the same time, there are so many ways to serve, and we all have different vocations, and it’s wonderful that women are taking leadership roles in such important organizations.”

Erin Saiz Hanna, executive director of the Women’s Ordination Conference in Washington, D.C., agrees that women leading Catholic organizations is worthy of celebration, but said the Church still comes up short when it comes to women because of its ordination rules.

“Women are told that they can be anything they want to be, and that any form of exclusion is ridiculous and unnecessary, so to see that discrimination in your Church is a complete disconnect from what makes sense,” she said.

Then there is the issue of what some see as a male-dominated culture among Church leadership.

Pope Francis has been taken to task for his off-the-cuff comments about women, avuncular in tone and extolling traditional roles for women. US Cardinal Raymond Burke recently suggested that an overly “feminized” Church has turned off boys and men from the faith, reducing an already diminished pool of potential priests.

“When you’re trying to talk about the Church as a place where women are valued and their talents have an outlet, you really have to take into account that these kinds of statements get a lot of attention and confirm what a lot of people suspect, that the Catholic Church is just really a hostile place for women,” Cummings, the Notre Dame professor, said.

When the Catholic Health Association bucked Church hierarchy by endorsing the Affordable Care Act in 2010, critics of Obamacare pounced on Sister Keehan. She said she enjoyed legitimate debate over ideas, but wondered if some of her harsher critics felt “more license to throw rocks at me because I am a woman or because I am a sister,” though she said she never interpreted the insults as misogynistic.

Even as the debate over the role of women in the Church simmers on, women are taking on higher-profile leadership roles, from parish administrators filling in for pastors to heads of major, multimillion-dollar organizations.

Sister Markham, who will replace the Rev. Larry Snyder at Catholic Charities USA on June 1, said she believes her female colleagues “would hope all of us do a good job regardless of our gender.”

Still, she believes her experience as a Dominican sister will help her lead the membership organization that represents and supports more than 70,000 employees in the United States, as well as lobbying on Capitol Hill.

“For us, it’s really the imperative we have as Dominicans to proclaim the Gospel message, that there is more life than death, to search for truth, and stand for justice in our world today,” she said. “That kind of grounding in Dominican spirituality has shaped my life.”

Several women interviewed by Crux said the Church must do a better job at highlighting the contributions of female leaders.

“There are many bishops who rely on the advice of women at every level, and I think they could be more open about that, talk publicly about some of their most trusted advisers who are women,” said Cummings.

Woo agreed.

“The Church could acknowledge the women who run the schools, balance the budgets, lead the hospitals,” she said. “Tell me, when was the last time you read an article that showcased women leaders in the Church?”