SAN FRANCISCO — When Max Hollein announced his idea two years ago for a sweeping exhibition of Muslim fashions at the de Young Museum here, where he was director, he received some “very intense reactions,” he recalled. And the criticisms came from surprisingly different factions.

“I got a number of emails complaining, some in very harsh terms, that this is not the right time for America to celebrate Muslim culture,” Mr. Hollein said. “On the other hand, there were also people accusing us of celebrating the oppression of women.” (Breitbart News Daily questioned whether it was “a celebration of subjugation.”)The museum also heard from people of Islamic faith who found the notion of “fashion” antithetical to the religion’s modest dress codes. For them, the very idea of the show seemed sacrilege.

“We knew from the start we were entering new territory,” said Mr. Hollein, now the director at the Metropolitan Museum of Art in New York, taking a break last week from his new job to attend the opening of “Contemporary Muslim Fashions,” his first — and last — major show at the de Young. Mr. Hollein was wearing a dark blue Zegna suit that looked rather plain compared to a peacock-colored gown on display nearby.

“The idea wasn’t to provoke,” he said. “We wanted to share what we’ve been seeing in Muslim fashion with the larger world in a way that could create a deeper understanding. Museums are one of the few places where you can have a deep and non-polemic debate about the intersection of cultures. On other platforms, people either have superficial conversations — or just yell at each other.”