Chromium is on the Red List* from Campaign for Safe Cosmetics, a project of Breast Cancer Prevention Partners (previously the Breast Cancer Fund). They classify the metal as a known carcinogen and developmental toxicant.
The European Chemicals Agency (ECHA) has no hazards registered in the classification of chromium.
* “The Red List includes chemicals found in personal care products that pose serious, chronic health concerns including cancer, hormone disruption, and reproductive and developmental harm. The list also flags chemicals that are banned or have use restrictions by the U.S. or other world governments, ingredients that adversely impact worker health, and ingredients that are widely used in products marketed to women of color.” – Campaign for Safe Cosmetics