Using the term "illegal" instead of undocumented immigrant is disrespectful and impolite.
How is that disrespectful and impolite? I mean, they immigrated illegally, so that's the most logical thing to call them. [This] just seems ridiculous and oversensitive.
The problem lies in judging someone's existence as "illegal".
So would 'criminal' immigrant be more sensitive? 'Undocumented' makes it sound like they merely forgot to file some bureaucratic form which would have automatically approved had they done so. 'Undocumented' is too much of an understatement to be correct in any manner save that of political correctness.