Wasn't the issue already decided by SCOTUS over a hundred years ago? :
"To hold that the Fourteenth Amendment of the Constitution excludes from citizenship the children, born in the United States, of citizens or subjects of other countries would be to deny citizenship to thousands of persons of English, Scotch, Irish, German, or other European parentage who have always been considered and treated as citizens of the United States." - Justice Horace Gray (United States v. Wong Kim Ark)
Besides the precedent I find it extremely unlikely that it would even be a 5-4 decision. 9-0 seems a lot more likely. It was 6-2 in 1898 in the case above. There's no way someone like Roberts is going to vote against birthright citizenship when the 14th amendment so clearly says "All persons born...in the United States...". Even a judge who's quite conservative like Scalia or Alito wouldn't rule to invalidate birthright citizenship, they would say you need to amend the constitution if you want that to happen.