Fashion is an embodied form of culture. It builds on intimate information about the wearer, concerning e.g. body shape, size, age, weight and style. As fashion is digitalized, intimate body data is shared in online environments, which raises novel concerns about the privacy of fashion consumers. This is especially visible in online shopping, which has revolutionized fashion retail and data collection practices in fashion, particularly as concerns the secure and fair use of consumer data. We argue that the datafication of fashion should be investigated as part of sustainability discourse, and data fairness be established as a responsibility criterion. We analyzed 32 popular Finnish online clothing stores. Data management was studied by analyzing the online stores' network traffic to third parties, investigating the transparency of their privacy policy documents and analyzing possible dark patterns in the website's cookie banners. Our findings raise concerns over data responsibility and privacy in various areas. The analyzed websites had a high number of third-party services, averaging 5.2. Only 17 online stores out of the examined 32 (53%) clearly mentioned that they collected identifying information and product information in their privacy policies, and only five of the stores (16%) had no dark patterns in their cookie banners. Our results also suggest that several brands that are otherwise considered ethical may need to pay more attention to their fair data processing and privacy. This indicates that a wider discussion about data privacy and data handling practices is needed. Fair management of data must be part of the process of evaluating the sustainability of clothing companies.