The election frontrunner, economist Javier Milei, opposes abortion and wants to hold a referendum on whether the 2020 legalization of abortion before the 14th week of pregnancy should be repealed. He also wants to shut the ministry of women, gender and diversity, which he has called a type of "affirmative action" that is degrading towards women.

His closest contenders are economy minister Sergio Massa for the incumbent Peronists and conservative ex-security minister Patricia Bullrich, the most high-profile female candidate. She would leave abortion laws unchanged, though also close the women's ministry.

Milei's stance has caused fears among feminists of a risk of backtracking on gains in women's rights in recent years, but has helped him win votes among young Argentine men who feel disenfranchised, as well as conservative female voters.

"The Milei phenomenon is not just an ultra-right movement. It is a patriarchal reaction against all the advances women in Argentina have had," leftist presidential candidate Myriam Bregman, who polls less than 5%, told Reuters.

Milei, the surprise winner of an August open primary, is riding high on backing from voters angry at 124% inflation, a painful cost of living crisis, and rising poverty. He has talked of waging a "cultural battle" against socialism and feminism.

Eugenia Rolon, a social media influencer who volunteers with Milei's campaign and identifies as anti-feminist, said policies to support women were "discriminatory."

"They ridicule the women who are part of the movement by, for example, demanding that women have public office by quota," said Rolon. "A woman should not be in power because she is a woman, she should be in public office because of her suitability and her capacity."

Milei's strident views - and those of his backers - have riled up opponents, with women marching in Buenos Aires in late September to mark International Safe Abortion Day, some carrying placards criticizing him and defending abortion rights.

Many wore green and waved green handkerchiefs, an echo of earlier protests that contributed to the 2020 law change and is sometimes known as the "green wave."

"Milei is another example of the patriarchy that wants to reverse our rights," said Nelly Borquez, a feminist activist at one protest. "But he is going to find us back out on the streets."

'THIS IS NOT BY MAGIC'

Milei's support is over 60% male, according to a poll by Taquion Research. Still, he has won over some female voters, and has high-profile women on his team, including his sister and campaign adviser Karina and running mate Victoria Villarruel.

"Javier doesn't hate women," said Valentina Brites, an 18-year-old law student, during a march in his favor, echoing his view that women were already empowered and so do not need a specific ministry. "The laws are there to protect us, and there's no need for a ministry to represent us," she said.

Milei's critics accuse him of ignoring the existence of gender violence and discrimination in Argentina, where last year a woman was murdered every 35 hours and women earn 27% less than men.

"He doesn't believe in equality, social justice or that gender violence exists," said women's minister Ayelen Mazzina, adding that she had invited Milei to the ministry to learn about its work, but that he had declined.

Argentina has led the region in progressive policies on gender equality and LGBT rights for years, becoming the first Latin American country to implement a gender quota law in politics in 1991 and legalizing same-sex marriage in 2010.

"This is not by magic," said Mazzina, adding it was the commitment of successive governments to close the gender gap that kept things moving forward. Massa would keep this going, she said, while Milei would be a significant setback.

"Where would these women ask for help? Where would they knock on the door?"

Bullrich would also close the women's ministry to reduce bureaucracy, but would prioritize fighting femicide, narrowing the gender wage gap and improving women's healthcare, among other policies, said Silvia Lospennato, who is leading Bullrich's gender policy.

Repealing the abortion law is not on their agenda, because "Argentina already had that debate," she told Reuters.

Lospennato, a congresswoman for the conservative PRO party, said Bullrich offered a middle ground between Milei's anti-feminist stance and the government's overly bureaucratic model.

"To improve the lives of Argentines, we have to improve the lives of Argentine women," said Lospennato. "We are half of the population and we have specific problems which need specific solutions."

(Reporting by Anna-Catherine Brigida; Additional reporting by Candelaria Grimberg and Lucinda Elliott; Editing by Adam Jourdan and Rosalba O'Brien)

By Anna-Catherine Brigida