Ms. Majeed, 25, challenged her sharply: “Don’t you think that it would create problems for Islam” for everyone to wear the niqab? “It is nowhere mentioned in Islam and does make our religion look bad.”

Crucially, Ms. Majeed contrasted the situation in Europe, where, she argued, life was hard enough without the question of the veil. “Some jobs you cannot get if you are not willing to take off the hijab,” she said, pointing to her headscarf. “People think of us as the scary Muslims, so we don’t need women to wear niqabs.”

Ms. Moyosore, 24, immediately shot back: “But who are you to decide? If a woman thinks she wants to wear it why shouldn’t she? If a woman in Afghanistan who has not been forced to do so believes she has to wear the burqa, then let her.”

Emotions and voices rose. Kurshid Ahmed, a Pakistani businessman, tried sarcastic humor to defuse the situation. “You know, in Pakistan we say there is much more corruption under the niqab,” he joked.

But the women went on undeterred with their debate.

“See, we would actually need an intrafaith dialogue,” said Deepika Nagabhushan, a businesswoman from Bangalore, India. “We all talk about tolerance and common ground between different religions, but what’s with the tolerance inside your own religion?”

She said she followed some aspects of Hindu tradition not out of belief but because she lives with her parents and does not want to disappoint them.

“We have a tradition which says that you are not supposed to touch anyone when you have your periods,” she noted.