I would imagine that many illegals avoid it thru fear.
If they're illegal, they will be fearful despite the census, as they can be
detained by immigration at any time, if found, but I get your point.
It was the job of census officials to reassure all people, wherever possible,
that completion does not mean any branch of authority, can access their data, it's totally secure and is purely for planning purposes, although some don't comply, I agree.
Many people who outright refuse are followed up, and will be fined and made to comply, and there are very good reasons for this. It's no good complaining that there is only one doctors surgery, or playing field, school, dentist or any any other service in your area if the govt is under the impression that only 10,000 people reside there and there are really 20,000, for example.
So just complete the form, it helps, and will never result in a knock on the door with some copper waving it at you and asking you to accompany him to the station.