AKSU, China—Western companies, including brand name apparel makers and food companies, have become entangled in China’s campaign to forcibly assimilate its Muslim population.

Adidas AG, Hennes & Mauritz AB, Kraft Heinz Co., Coca-Cola Co. and Gap Inc. are among those at the end of the long, often opaque supply chains that travel through China’s northwest region of Xinjiang. Residents there are routinely forced into training programs that feed workers to area factories, according to locals, official notices and state media.