An administrative determination, such as an executive order, would be challenged in a lower court, and overturned.
The only way to strip citizenship away would be to amend the Constitution to clarify the language in the 14th Amendment.
Even so, it couldn’t be applied retroactively, in keeping with the prohibition of ex post facto laws.
The law will not have changed, just the perceived status of the individual who incorrectly acted on a mistaken belief.
This is ADMINISTRATIVE DUE PROCESS not JUDICIAL PROCESS. They are very different parts of "governing".
Further, as long as ADMINISTRATIVE DUE PROCESS has not been exhausted, there is neither an error in the initial determination, nor in the subsequent determination, to be appealed to a federal court. That would mean that once you've lost the citizenship you didn't really have in the first place you may then apply for immigration, and then citizenship. The door is open!
There are a myriad of steps to go through before you could even get close to the issue of "anchor baby", and by then both your purse and your time on this Earth would undoubtedly be exhausted.