When a fashion industry sustainability group called out China over its treatment of Uyghur Muslims, the idea was to nudge Beijing toward human-rights reforms while cleaning up a troubled corner of the $60 billion global cotton business. Western brands have learned the hard way that things don’t work that way in China.

In the 12 months since the Better Cotton Initiative (BCI) — whose members range from Uniqlo owner Fast Retailing Co. to Nike Inc. and Walmart Inc. — published a statement on allegations of forced labor in China's cotton-growing Xinjiang region, several brands have suffered major setbacks in the country, which one of the world’s biggest producers and consumers of the fabric.

The organization missed production targets last year and companies including Levi Strauss & Co. and Chinese sneaker-maker Anta Sports Products Ltd. have scaled back their involvement.