Kazan, Tatarstan—Shelves of vodka line a shop wall in Kazan, the capital of the Tatarstan republic. Just opposite, Islamic prayer beads sit in heaps on a rack. In this Russian-ruled region with a Muslim majority, bars and mosques exist side by side. A nearby store advertises clothing for Muslim women, and inside, Zulfia, one of the two female owners, helps customers with traditional headscarves and brightly colored skirts. Since she opened the store nine years ago, Zulfia says demand is increasing as women embrace Muslim traditions with a modern twist. Outside, the Kazan Kremlin, a citadel home to Tatarstan’s president, stands elevated on the banks of the Kazanka River where its Islamic minarets and Orthodox domes overlook the city.

A federal republic within Russia located 500 miles east of Moscow, Tatarstan has long been a model region for religious and ethnic...

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