Well, maybe not for immigrants so much as for illegal immigrants, which is sort of the point, right?
In my experience, legal immigrants in particular respect the "stigma" against illegal immigration, which helps explain why they came here legally in the first place. If I were to write about a "pedophile football coach," I suspect that very few people would assume I was stigmatizing all football coaches.
Moreover, "stigma" is the wrong word. Stigma implies social condemnation, a public disgrace or reputational stain. "Illegal" is a legal term, meaning, er, illegal. For some reason, a lot of people insist that the "illegal" in "illegal immigration" is in effect an unfair slander. But we live in a country where illegal and immoral only occasionally overlap in the popular mind. How immoral it is to immigrate illegally to the country is debatable, but that it's illegal to do so isn't debatable, it's axiomatic.
Ironically, if we actually erased the difference between the legal and illegal immigrant, the result would be to stigmatize legal immigrants unfairly.
That won't happen, of course, because we'll still need a word for people who move into the country unlawfully. And whatever term we choose will soon enough be denounced as "stigmatizing."
Which brings me to the No Labels crowd. As far as I know, they haven't sounded off on this particular issue at all. But they do represent an approach to public policy that says our disagreements are the result of getting too caught up with ideological "labels." Put the labels aside, they say, and look at all of the problems we can solve! Invariably what this really means is, "If you drop your principled objections to what we want to do, we can finally do what we want to do."
Among the myriad problems with this insipid sophistry, the simple fact is that we need labels to think clearly and make distinctions. To its credit, the AP Stylebook still recognizes this. It just made things a little harder for everyone.