The executive order is, of course, legal gibberish. It does not say that the subject child is not a citizen, just that, under this President, it is "the policy of the United States" to pretend that he or she is not a citizen. The order thus violates the Equal Protection clause, not the birthright citizenship clause.
The order is just political eyewash. Ask the administration whether it's legal, and the mouthpiece - I saw VP Vance - launches into a long filibuster on what the law OUGHT to be. Many Americans reject the idea of anchor babies, so the order creates an opportunity for the MAGA pols to play to the MAGA base.
Legally, though, it's a nothingburger.