There is a parallel case about the legality of a nationwide ban on the EO over the 14th. In the discussion linked upthread there were some very interesting issues flagged up. The TL;DR is SCOTUS were asking whether the national Federal ban (imposed by a Federal court) was appropriate, if there were other ways to achieve the same end. And they rather skewered the Trump lawyer who was unable to suggest any. Also, the harm being done was so egregious that only a ban serves to avert it.
The interesting - and not really highlighted - possibility that a baby could be born in the US, and not only not be allowed to be a US citizen, but also not allowed to be a citizen of the country of either of it's parents (because they are refugees) was raised. With the possibility that without a nationwide ban, one state court might implement a ban, but another wouldn't, leading to further confusion over what state a baby was born in.
Note: that case is not about the 14th amendment, Just the nationwide ban until SCOTUS acts (which one of the supremes admitted could be "whenever").