When Zehre Avci, a daughter of Turkish immigrants in Belgium, was nine years old, she was sent to buy a coffin for her grandmother, who had just passed away. “I was crying,” she recalled. But she had to go, because “there was no one else to translate.” As a young teen, she led Turkish immigrant women with abusive husbands to get help for the same reason: There was no one else taking on the challenge.

Avci, now in her early thirties, said those experiences — doing what others cannot or will not do — inspire her current work in Brussels, where she has joined a social services agency dedicated to bridging the religious, social and economic gaps between immigrant women, many of them Muslim, and the wider Belgian population.

Like the more than 20 other Muslim women from around the world who gathered in Washington, D.C., this summer for a law and leadership program, Avci’s vision involves both leading her own Muslim community in more egalitarian directions and pushing for a deeper understanding of Muslims by…