The Constitution is, as ever, remarkably vague, but the process of the Census is politically vital. According to the Supreme Court in Baker v. Carr, we are supposed to have equal population between districts, and we allocate congressional districts across states by population (apportionment). Then, there is funding. Federal money is allocated based on population for a lot of stuff. The interesting thing about how the population rule works is that even people who don't get to vote are counted, even for representational purposes.
From a democratic theory perspective, this is kind of odd. My region gets a certain number of representatives based on the total number of people in it, and people who don't get to vote count. If you find yourself thinking back to the counting of slaves as 3/5 of a person for such purposes, giving a mathematical advantage to slaveholders, well...
Suppose you have a population that consists of eligible voters and ineligible voters, but the ineligible voters are non-randomly distributed geographically. If ineligible voters are "counted" in terms of apportionment of congressional districts across states, and "counted" in terms of population of districts because under Baker v. Carr, districts must have equal population without distinguishing between eligible and ineligible voters, then the eligible voters in the regions that contain disproportionate numbers of ineligible voters have their votes counted more because they are a higher proportion of the eligible population in their districts.
Put simply, if I live in a region in which 20% of the people are ineligible to vote because they are not citizens, and I am part of the 80% who are citizens, then I have more weight attached to my vote than someone who lives in a district with the same total population but where only 2% of the population are non-citizens.
Notice what I did there. I sidestepped the entire bullshit issue of non-citizen voting. Illegal immigrants aren't trying to vote. We don't have a voter fraud problem. That whole thing is a bunch of bullshit. Go read Justin Levitt's research on the subject. Trump is a lying sack of shit, but there are real, mathematical questions here.
Of course, we can apply the same logic to children. Anyone under 18 doesn't get to vote. The same logic can apply to convicted felons in states without re-enfranchisement, or anyone in prison, and... how do we count prisoners? Where are college students counted, just to name an issue that is directly related to my line of work?
When it comes to questions of population and allocation of resources, apportionment, etc., what is the standard, or what should it be? Equal raw population? Equal population over 18? Equal citizen population? Equal citizen population over 18? Equality of eligible voter population? Equality of likely turnout, based on the observation that likely turnout varies across districts given demographics? What about resource allocation? Lots, and lots, and lots of legitimate questions here.
When it comes to resource allocation, though, consider this. There are institutions like hospitals that get federal funding. People show up whether they are citizens or not. Those institutions need to be able to serve their populations, unless you want people with communicable illnesses out and about... That requires a count. An accurate one. Any method of counting likely to under-count high-need populations creates a potential problem.
Gee... I wonder if asking about citizenship status in mixed-status households when people are afraid of the government might lead to under-counts...
Anyway, even if we understand that Trump is a lying sack of fucking shit, there are some real questions here.