As much as I prefer the innocent child not have a label like that, I’ll go a little off on a tangent and say I think the US should seriously reconsider their possibly that being born here makes you a citizen (jus soli). Most of the countries in the Americas, the new world, had and have that policy for a variety of reasons, one obvious one is the Americas had so much immigration, but many other countries don’t have that policy.
I guess you can say first generation child of illegal immigrants? A new one or two word term or expression? I can’t think of anything. We did switch from illegal alien to illegal immigrant, maybe someone will come up with something besides anchor baby one day that catches on.
I can’t remember saying anchor baby, I don’t use that expression.