You can be a natural born citizen either by being here when born or by being born to a US citizen. The order challenges the former.
I saw people accurately predict that they would hang such an order on the "and subject to the jurisdiction thereof" portion. The argument was predicted to be that a mother on US soil unlawfully is excluded by that clause (though they are clearly subject to the jurisdiction despite being unlawful, this was the guess).
They are trying to push it even further by claiming people here legally also don't get the right, and there's not even a hint of rationalization to claim that somehow people legally here are not "subject to the jurisdiction".
That doesn't clear too much for me. Are you saying that everybody needs to go through the citizenship process and take the citizenship test? I'm not sure what the part about "subject to the jurisdiction thereof" means exactly.
Right now just being born on US soil automatically makes you a US citizen, regardless of if your parents are or not. It works that way in a lot of countries. I knew a guy in school who's parents are both British, his mother started giving birth to him on a plane so they did an emergency landing in Cyprus. Due to being born there he has both British and Cypriot citizenship.
This change would stop that happening in the US. Your parents would have to be citizens for you to become one as soon as you're born.