Leftists speak about "due process" as though it were a fixed package of processes and procedures. That is manifestly not the case.
Due process for an American citizen accused of a crime is what they are thinking of, but that level of formality is not required for, for example, POW's, non-citizens crossing our border, non-citizens apprehended inside the U.S., or people who remain after their visas have expired. Due process for an illegal who is charged with a crime is not the same as due process for a citizen; s/he can be deported quickly, without a trial, and certainly not a jury trial. And "proof beyond a reasonable doubt" is definitely not the standard of proof.
The "due process" that illegals are entitled to when not actively committing a crime - just going about their business is not a simple matter, and THIS President, who campaigned on a promise to remove as many illegals as possible is right to take an aggressive stance on how to go about it. If the USSC intervenes, that's a different matter, but there are no definitive guidelines yet.
Regardless, U.S. District Court judges are traveling far outside their lane when trying to dictate these matters to the President of the Fucking United States.