The school of thought is that they have to be specific to areas of current Law, but that is as vague as what constitutes a Natural Born Citizen.
FDR issued thousands of EO’s with the most famous being the Internment of Japanese American Citizens. I guess if Lincoln could ignore Habeas Corpus and imprison his Political Enemies during the Civil War, anything is fair game.
EOs are constitutional only insofar as they are used to manage how the Executive branch operates. They are not constitutional if they change duly passed statutes or bypass the other two branches of the government.