In the US there is a lot of law that makes employment discrimination illegal for a number of classes of people.
IANAL: I don't know if it is outright illegal to request a picture but it sure seems like a great way to open yourself up to a lawsuit.
> Title VII of the Civil Rights Act of 1964 (Title VII), which prohibits employment discrimination based on race, color, religion, sex, or national origin
> the Equal Pay Act of 1963 (EPA), which protects men and women who perform substantially equal work in the same establishment from sex-based wage discrimination
> the Age Discrimination in Employment Act of 1967 (ADEA), which protects individuals who are 40 years of age or older
> Title I and Title V of the Americans with Disabilities Act of 1990, as amended (ADA), which prohibit employment discrimination against qualified individuals with disabilities in the private sector, and in state and local governments
> the Civil Rights Act of 1991, which, among other things, provides monetary damages in cases of intentional employment discrimination.
https://www.eeoc.gov/facts/qanda.html