“Illegal aliens are not under the jurisdiction.”
Cool, so they can’t be arrested for breaking our laws then. That’s what you are saying.
Illegals are subjects of the country they came from. In other words, Mexicans who enter illegally are STILL Mexican citizens. They are NOT USA citizens just because they crossed the border. They still have allegiance to Mexico.
As to whether they have diplomatic immunity, no because they are not registered agents of Mexico otherwise they would be able to commit crimes and not be arrested (just like diplomats). Being a non-registered agent does mean they are “under the juristiction”.
You go and try giving birth in Mexico to see if they give your kid automatic Mexican citizenship. It ain’t happening.