Why do I care what the UN's preferred wording is?
You made a false claim about the origin of the terminology. You should care about being factually accurate.
The correct and proper legal term in the USA is "illegal alien"
It literally is not. That term, while it exists in the US code, is incommon. The most common term in the US code is just "alien", and when specifically discussing the undocumented, "Unauthorized Alien". I didn't include a discussion of US code just so you could pretend it didn't exist.
And I'm sorry if you don't like being called out for wanting cheap, exploitable labor to pick your damn cotton,
I'm struggling to understand what your argument is. You seem to be declaring that any job involving cotton is inherently slavery, even if the people are free to come and go as they choose and are paid for their labour. If that's not your argument, then please clarify, as otherwise, I'm baffled.
Democrats want cheap labor they can exploit.
Democrats (aka, the party that is constantly pushing for bills for higher minimum wages and mandates for better working conditions, while the Republicans do the opposite, pushing deregulation) want above all a regularized system with rules and oversight to prevent abuses. Most also want a path to citizenship for people who work for a given number of years with no criminal record (7 years is a common number suggested, though even decades would be better than "never"), though this is secondary to the primary issue. What Democrats do not want is a masked gestapo kidnapping people who want to be in the US working, from in front of their children, and throwing them into "Alligator Alcatraz".
These things are the exact same thing that the immigrants themselves want. You can't sit here and pretend to be an advocate for immigrants when arguing for policies that they are opposed to and opposing policies that they support.