FORT MORGAN, Colo. — The work is far from glamorous: The thermostat for much of the slaughterhouse is set near freezing, the clatter of machinery is almost deafening, and there is the matter of slicing cattle carcasses every day, eight hours a day.

But for the Somali refugees who settled in this community on Colorado’s eastern plains, jobs at Cargill Meat Solutions had become a path to the American dream. The positions started at $14 an hour, required little English and, for the most part, allowed time for prayer, in accordance with workers’ Muslim faith.

“If I can pray, I will do whatever they need,” said Abdukadir Ali, 28, who used to cut fat five days a week, wearing a metal protective vest and gloves three layers thick.

In mid-December, a dispute erupted between Muslim employees and Cargill managers over the role of prayer in the workplace. Employees say top managers told them that their religious breaks — previously allowed once or twice per shift, in 10-minute segments, after explicit permission from a supervisor — would be severely curtailed.