Amazon Chief Executive Jeff Bezosrecently called the conflict between privacy and security an “issue of our age.” But while he says Amazon will fight government investigators who try to obtain personal information from devices made by his company, Amazon is marketing face-recognition technology to private businesses and law-enforcement agencies alike, for uses that many believe are a threat to privacy.

Face recognition is a stark example of a technology that is being deployed faster than society and the law can adopt new norms...