Sorry, but Plyler v. Doe had to do with public education rights for illegal aliens, not birth rights.
The current birthrights are written into US Constitution, and have yet to be argued in the Supreme Court. Although it will be soon.
So, no illegal aliens gain entry by birth.
?
While the SCOTUS has not directly addressed the issue in an adverse finding it has offered it's opinion. The children of illegal aliens are not subject to the jurisdiction of the state in which they reside and therefore not protected by the provisions of the amendment. The myth that these children are automatically granted citizenship is rather recent folklore. The 1982 decision avoided directly addressing the issue of the rights of this suspect class and instead addressed the ability of states to protect themselves from illegal immigration.
Adding to the confusion, the 14th Amendment was never constitutionally adopted. It was ratified by less the 3/4 of the states, even excluding the antebellum states, and was certified by an individual who lacked the constitutional authority. Probably one of the worst examples of the tyranny of the majority: a Republican majority.
The irony is that this tyranny may well be the undoing of the republic given the increasing politcal power of this suspect class.