Oh you don't need to comment on anything in those posts. Nothing in there is legally sufficient or shows any understanding of how the courts interpret the Constitution. Neither the poster or the writer of those articles should be doing any homework for anyone about these issues.
As a note, this is not really about due process. Just that the type of issue that would be brought up has relatively little legal history. It's quite possible the SC wouldn't even take the case because of past court precedent. There isn't much legal scholarship suggesting that the 14th Amendment doesn't encapsulate birthright citizenship. The argument the court would possibly take on is whether or not "subject to the jurisdiction of" covers those that enter illegally. I don't think that argument has too much weight though because no one would suggest that if someone illegally entered and committed a crime, that the US wouldn't have jurisdiction to prosecute. TBH that statement was mainly meant to say that foreign diplomats and indigenous tribes were not covered by this. While being within the physical jurisdiction of the US, they were subject to other powers.
This link paints a pretty good picture of what you are talking about and I believe if Trump wants to go down this route, if anything the case would be if he actually have the authority to even do this based on an EO.
When all is said and done, if people really want to change how this amendment is worded or restrict its meaning, it sill needs to go through congress and ratified by the states.