One poster read: “Keep your dick pics to yourself.” Another had a drawing of a vagina and two ovaries and the words: “Grow a pair!” A third said, “If you like the headscarf so much, tie it around your eyes.”

The posters featured at women’s day marches across Pakistan last week, and were just a handful among hundreds that highlighted fundamental rights issues such as access to education and employment. They have since unleashed a social media storm. Thousands complained the marchers were “vulgar” opportunists who had infringed on conservative values in the Muslim-majority country and supplanted a legitimate fight for rights with a liberal, anti-Islamic agenda. Many called for a parallel men’s march.

Shaan Shahid, arguably Pakistan’s biggest film star, wrote on Twitter he thought the posters did not “represent our culture, our values”. Veena Malik, a popular actor who caused an uproar in 2012 when she appeared almost naked on the cover of an Indian men’s magazine, posted that the march had “brought humiliation to women of Pakistan”.

Kishwar Naheed, a poet best remembered for a poem called “Us sinful women”, was seen in a video saying: “The next time you make such slogans, remember your culture, your traditions.”

Some of the profanity-filled tirades were more frightening. Javeria Waseem, a film student, posted screenshots of a group of boys sexually harassing her 16-year-old younger sister online and threatening her with rape for posting on Instagram in support of the march.

Nighat Dad, a rights activist who was photographed holding a poster that read: “Divorced And Happy”, received messages filled with sexual innuendo and threats of sexual violence.

At least seven women who attended the march in Lahore and did not want to be identified told the Guardian they had received threats of physical and sexual violence from social media users after posting pictures of the posters.

Pakistani women participate in a rally in Karachi. Photograph: Shahzaib Akber/EPA

In Pakistan the threats of violence are not hollow. About 500 women are killed each year by family members who believe their honour has been damaged, according to the Human Rights Commission of Pakistan.

‘You can’t say you are happily divorced’

Dad, who organised the women’s march in Lahore, said people were angry over the posters because most Pakistanis, especially men, could conceive of better school and workforce participation and parliamentary seats reserved for women, but were not yet ready to allow them free choice.

“When women make demands about their personal lives, their bodies, their sexuality, that’s when people feel threatened,” Dad said. “So it’s OK to ask the government for the right to education but you can’t say you are happily divorced because the breakdown of a marriage is a shameful thing, a woman’s failure, and you can’t say ‘don’t send me dick pics’ because so-called respectable women don’t use words like dick.”

It made sense, then, that the posters that got the most vitriolic responses were “those that spoke to the intimate relations of power within the household”, said Nida Kirmani, a feminist sociologist at the Lahore University of Management Sciences.

One popular poster called for men to warm their own food; another asked them to find their own socks. And one read, “I’ll warm your food but you warm your own bed.” .

“Of course these kinds of slogans have unleashed a wave of masculine anxiety,” said Sabahat Zakariya, a newspaper editor who runs a YouTube channel to explain feminist theory.

An International Women’s Day march in Karachi, Pakistan. Photograph: Shahzaib Akber/EPA

“The home is the seat of masculine power and the posters hit right at the heart of that,” she said. “Men are afraid that women will now also start asking for rights within the home; they will question why they should stay in abusive marriages or always be the ones who cook. That’s a lot scarier for some people than sending girls to school or letting them work.”

But Dad called the protests “a great start”.

“It is a huge success of the march that taboo topics like women’s rights to their own bodies, their sexuality, are being discussed for the first time.”