BOSTON — In a test of Harvard’s famed open-mindedness, the university has banned men from one of its gyms for a few hours a week to accommodate Muslim women who say it offends their sense of modesty to exercise in front of the opposite sex.

The policy is already unpopular with many on campus, including some women who consider it sexist.

“I think that it’s incorrect in a college setting to institute a policy in which half of the campus gets wronged or denied a resource that’s supposed to be for everyone,” a student who also wrote a column in the Harvard Crimson newspaper critical of the new hours, Lucy Caldwell, said.

One student, Ola Aljawhary, who is Muslim and works out elsewhere on campus but is not one of the women who requested the change, rejected that argument. “The majority should be willing to compromise,” she said. “I think that’s just basic courtesy. We must show tolerance and respect for all others.”

The trial policy went into effect February 4, about a month after a group of six Muslim women, with the support of the Harvard College Women’s Center, asked the university for the special hours, a spokesman, Robert Mitchell, said.