In an article by the U.S. Food and Drug Administration, there is evidence that supports your claim that food dyes can pose health risks. However, it does depend on the amount of dye and how they are being used. Linda Katz, M.D., M.P.H., director of the U.S. Food and Drug Administration’s Office of Cosmetics states, “Color additives are safe when used properly" and "There is no such thing as absolute safety of any substance". The FDA does regulate color additives used in the U.S. in foods, drugs, cosmetics, and more. Because color dyes can be so harmful and cause many health problems, the FDA does not approve color additives that the agency has found to cause cancer in animals or humans. The article discusses possible reactions to color dyes, like itchiness and hives from FD&C Yellow No. 5. Clearly, food dyes can be unhealthy and pose health risks in many scenarios. It is important to know if your products are FDA certified and what you are actually putting into your body.
https://www.fda.gov/consumers/consumer-updates/how-safe-are-color-additives