Read the text:
Sec. 2. Policy. (a) It is the policy of the United States that no department or agency of the United States government shall issue documents recognizing United States citizenship, or accept documents issued by State, local, or other governments or authorities purporting to recognize United States citizenship, to persons: (1) when that persons mother was unlawfully present in the United States and the persons father was not a United States citizen or lawful permanent resident at the time of said persons birth, or (2) when that persons mothers presence in the United States was lawful but temporary, and the persons father was not a United States citizen or lawful permanent resident at the time of said persons birth.
It says nothing about local jurisdictions. What would this cover? Soc. Sec. cards. Passports. Military ID, I guess. That sort of federal document. Don't know how they check citizenship when you apply for them if the birth certificate doesn't state.
(c) Nothing in this order shall be construed to affect the entitlement of other individuals, including children of lawful permanent residents, to obtain documentation of their United States citizenship.
Worth pointing out.
Sec. 3. Enforcement. (a) The Secretary of State, the Attorney General, the Secretary of Homeland Security, and the Commissioner of Social Security shall take all appropriate measures to ensure that the regulations and policies of their respective departments and agencies are consistent with this order, and that no officers, employees, or agents of their respective departments and agencies act, or forbear from acting, in any manner inconsistent with this order.
(b) The heads of all executive departments and agencies shall issue public guidance within 30 days of the date of this order regarding this orders implementation with respect to their operations and activities.
Again, it applies to federal agencies and such. Not your local county or city or state registrar.
And the "public guidance" doesn't say that "their" is local or state government. Don't know if the guidance has been issued or not, you'd think that would be reported but it would be immensely boring and of little interest, when it obviously applies mostly to various agencies. The one exception would be Social Security, and that was a big deal months ago when the EO took affect. Medicaid's state run, not federal, don't know how that would be handled, what the state-federal interface for that program is.