No one is stripping citizenship from citizens. People love to put words in other peoples’ mouths.
So the children born of illegal immigrants get to 1.) stay and 2.) keep their citizenship?
If you don’t want them to 1.) stay, but do want them to 2.) keep their citizenship, do you then deport an American citizen?
If so, what is the cut-off age for those US citizens (born to an illegal) that would then be deported? Those 18 and under? 10 and under? 5 and under?