A group of religious and socially conscious investors and other funds are ramping up pressure on Western companies over alleged human rights abuses in China's Xinjiang region, highlighting the challenges for brands trying to maintain their business ties amid rising tensions.

The group of more than 50 investors, backed by the Interfaith Center on Corporate Responsibility, said it is in the process of contacting more than 40 companies, including H&M, VF Corp., Hugo Boss and Zara-owner Inditex, requesting more information about their supply chains and urging them to quit situations that could lead to human rights abuses.

Anita Dorett, program director for the Investor Alliance for Human Rights, which put together the request to the fashion brands and other big corporate names, said she was worried that some companies had moved to scrub language about policies on forced labor from their websites, or pledged to buy more cotton from Xinjiang, in fear of a backlash from Chinese social media and companies.