From a point farther up the path, several hundred men screamed at the woman, insisting that she immediately turn back from visiting the Sabarimala Temple, a centuries-old shrine in southern India. When the pair of visitors, both journalists for The New York Times, decided to descend, the crowd rushed at them, hurled rocks and pummeled two dozen police officers.

“Madam, you don’t be afraid, O.K.?” Habeeb Ullah, one of the police officers, told one of the journalists, a bit too late.

For centuries, women of childbearing age were prohibited from entering the temple, which is perched on a lush hill in the coastal state of Kerala. Last month, after India’s Supreme Court struck down that ban, saying that barring women from the temple infringed on their constitutional rights, thousands of protesters pledged that women who dared to visit the temple would be punished.

“Hooliganism reigns in this place,” the woman’s father, Manoj, who goes by one name, told the Indian news media. “It’s almost as if these people view women as terrorists.”

By late Wednesday, the Kerala government had deployed hundreds of heavily armed police officers near a river bed at the base of the trek, and dozens of people had been arrested. Manoj Abraham, a police officer in the area, said, “Every devotee will be allowed safe passage.”

But the dispute is about something much broader than access to a temple: whether Supreme Court rules can be enforced in a spectacularly diverse country of 1.3 billion people, where progressive court orders issued in New Delhi are abstract, or optional, in rural parts of India, and communities are intensely organized around religion.

Though Indian women are leading campaigns to dismantle discriminatory rules on access to religious sites, and courts are ruling in their favor, the grip of tradition is still ironclad in places like the Sabarimala Temple. “In India, the people’s belief is more important than any law,” said Devidas Sethumadhavan, a district officer in Kerala for the Rashtriya Swayamsevak Sangh, a right-wing Hindu nationalist group.

But in September, the Supreme Court overturned a 1991 decision by the Kerala High Court, which had upheld the ban. The Supreme Court ruled 4 to 1 that preventing menstruating women from visiting the shrine violated the country’s Constitution and was similar to the ostracism faced by India’s lowest castes, formerly known as “untouchables.”

“This denial denudes them of their right to worship,” Chief Justice Dipak Misra, who has since retired, wrote in his opinion.

In a concurring opinion, Judge Dhananjaya Y. Chandrachud wrote: “To treat women as children of a lesser god is to blink at the Constitution itself.”

Around Kerala, the ruling brought a wave of anger, particularly among far-right Hindu nationalists affiliated with India’s governing Bharatiya Janata Party, or B.J.P., which rose to power in 2014 with the election of Prime Minister Narendra Modi.

Members of the B.J.P. and other political parties have demanded a review of the court’s order. But Kerala’s chief minister, Pinarayi Vijayan, who accused fringe Hindu groups of backing Wednesday’s attacks, said the state government would do everything in its power to uphold the Supreme Court’s ruling.

“Those who want to pray cannot be stopped,” he said.

For the Times journalists, the problems started before the trek had even begun. Early Thursday morning, when they walked toward the starting point, a group of young men asked where they were going, where they were from, and if the woman, 46, had an identification card.

Later, with cameras from several local television stations surrounding the journalists, a group of men started chanting “Go back!” and “Leave!” in Malayalam, a local language, and English.

Along the trek, framed by views of thick forest and cubbyhole restaurants selling lemon soda and snacks, the intensity of the attacks grew more acute and better organized. After a bare-chested man, muttering under his breath and wearing a saffron scarf, a politically charged symbol for Hinduism, pointed his cellphone camera at the woman, a long line of men began doing the same, and then they followed her.

Past the halfway point, a larger crowd higher on the hill started screaming, raising fists in the air and jumping on the trail’s side railings. When the journalists decided to turn back, the protesters, apparently emboldened, started chasing them.

Police officers braced for the impact, swatting the air with wooden batons. Several of them insisted that it was still safe for the pair to continue, even as they struggled to hold the crowd back.

At one point, a group of men broke through the clasped hands of the officers, who had formed a ring around the woman, and threw rocks at her. She was struck on the shoulder but was not wounded.

At the bottom of the hill, heavily armed officers ushered away the two journalists, who were escorted from the area in a caged bus.

The police said that no woman had gotten so close to the temple in more than two decades.

Officers said they were not sure what would happen in November, when traffic to the temple picks up enormously, and when pilgrims often wait 10 hours just to start the hike. In previous years, women under 50 might have gone unnoticed in the crowds, the police said, but this year, with tensions raised, greater scrutiny is expected.

Still, there were a few small signs of encouragement. As the female journalist neared the bottom of the trail, an angry group trailing her, a small man pushed past a police officer, stuck out his hand and smiled.

“I want to congratulate you,” he said.