Relatives of workers who died in April in the collapse of a Bangladeshi garment factory gathered to demonstrate.

Finding ethical clothing—apparel produced according to fair labor standards—can be difficult. The prevalence of fast-fashion emporiums and the ubiquity of $5 T-shirts at stores such as Costco and Walmart make the task especially challenging.

But in several studies, consumers have indicated a distinct interest in buying ethical clothing. In one recent Ipsos poll, 40 percent of respondents said they were indifferent about how and where their garments were produced, but 70 percent said they would be willing to pay extra for ethically sourced apparel.