I, personally, do not believe there is any disagreement between the Constitution and GDPR. In fact, a right to privacy has long been inferred by combining traits of a few amendments: https://en.wikipedia.org/wiki/Right_to_privacy#United_States (Of course, that constructed right is a right to privacy specifically from government actions.) And generally, we've recognized that some rights such as speech, may need to have limits to avoid encroaching upon other rights, such as privacy.