I disagree with this; this is the primary means by which dehumanization occurs. I like to think of "police officer" as the perfect dehumanizing term because it showcases that dehumanization is not always negative. Some people will hear the term and automatically think good things and some will automatically think bad things. Few will think about a person they don't know, complete with vices and virtues they may or may not agree with. The point is that dehumanization makes you think of a concept of a person rather than a person.
So I think that dynamic is present in every term we use to refer to humans as something other than "human". I don't need people to refer to me as "human who programs computers" so that I'm not dehumanized. (In fact, once "human that programs computers" becomes the accepted term, that term would also have the dynamic of dehumanizing those it covers. Having the word "human" in it wouldn't save it once it became a recognized term.)
That is not what is said - otherwise it would be people who immigrated illegally, using an adverb instead of an adjective.
By moving the designator illegal from the activity to the person, you are criminalizing their being instead of their deed.
Now, you can say that the immigration laws are morally wrong if you want, but that's a different argument. As far as descriptive terms go, they immigrated illegally, so they're illegal immigrants - immigrants whose immigration was illegal. No, we're not going to go with whatever newspeak alternative you come up with.
But your side also has a valid point: These are human beings. They deserve to be treated like humans, not animals, even if they are being expelled from the country. That's a true point, and one that needs to be made repeatedly. But heckling people about the term used to describe the people is not going to move the needle on that issue.