PIESTANY, Slovakia — Why so many wealthy Arabs have chosen Piestany, a pleasant but faded little spa town, as a vacation destination is something of a mystery.

Some say it started in the 1960s, when aspiring pilots from the Middle East came for flight training at the nearby airport. Others point to a Slovak soccer coach who went to Qatar decades ago and inspired visitors.

Whatever the case, every summer, they come by the thousands.

The town’s spas stretch along a narrow island opposite the city center, presided over by the Hotel Thermia Palace, the grandest of the venues and once host to European royalty and Indian maharajahs. Now it is more likely to attract a Kuwaiti princess, as the town’s central pedestrian strip has turned into an unlikely panorama of Muslim women in traditional dress and men smoking hookahs outside kebab shops.

It was never a problem. Until now.

The populist wave that has swept Central Europe — fueled by a backlash to the refugee crisis — is affecting even this pampered cocoon of transnationalism that depends utterly on well-heeled visitors from abroad. The hint of menace has unnerved and surprised regular visitors.