[Grustaf]

The common objection to "illegal immigrant" is of course to say that "people are not illegal", and strictly speaking a more grammatically correct term would perhaps be "illegally immigrated".

But this is a mostly irrelevant objection, the same construction is used in other phrases, including "undocumented immigrant". It's not the person that is necessarily "undocumented", it's their act of immigration, and everyone understands that.

[ALittleLight]

That is commonly what people say, but as you point out I don't think their objection is consistent. You might call someone who perpetrated an act of violence a "Spouse abuser" even if that person spends 99.9% of their waking hours not beating up their spouse.

Calling someone a spouse abuser, drunk, jaywalker ("Nobody actually walks jays!"), illegal immigrant, whatever doesn't at all imply that you are summing up the totality of that person as all and only that appellation. It just means you think they've committed the associated crime. It would be rude to call an illegal immigrant an illegal immigrant at every opportunity, but it is just dishonest in my view to assert that they are not an illegal immigrant.