The census has been a bit of a political football for decades.
The last big battle was during the Clinton years, when the bureau wanted to start wide spread statistical adjustment on the census numbers, and to use those adjusted numbers across the government. The reason for this was simple...since there's no way to count everyone, you adjust the numbers to make up for the people you can't count. Simply put, if you had a neighbourhood with ten blocks, and you could only count nine of them, you take the demographics from the nine you did count and impute them to the tenth.
The issue was, it's often minority, immigrant and poorer areas that are the most undercounted. So by essentially "creating" more people via statistical adjustment, this would theoretically increase the numbers in places that tended to support Democrats. Naturally, Republicans cried foul, and the case eventually made its way to the SCOTUS, who more or less handed the GOP a victory. They said the Census Bureau could use adjusted numbers for things like allocating federal resources, etc., but not for purposes of Congressional apportionment (the Constitution requires an "actual" count), which is what Dems really wanted and the GOP hated.
So this is more politics. On one hand, it seems that yes, it's a political move designed to help Republicans and there may be an ulterior motive (in fact I'm sure there is). But there are all kinds of questions asked on the census form (particularly the long form), that go beyond simply counting you as a person, and the government uses the data for all kinds of reasons. Of course they can ask about citizenship status (it's been done before). The suggestion that asking the question is unconstitutional is ludicrous, and I doubt any of these lawsuits will get very far (well maybe they'll have some temporary luck in the 9th Circuit). The Constitution makes clear that the census falls purely into the purview of the Federal Government, and the states have very little to say about it. It is the Federal Government, after all, that determines who can be a citizen, lawful resident, etc.
I do think the argument that the question might make some immigrants less likely to talk to census workers is a valid one...I'm sure that will happen to some extent and that could result in a less accurate count. So while it may be bad policy, it's not unconstitutional...there are lots of bad policies that are nonetheless perfectly Constitutional.
So yeah, I personally think this is bad policy and at least partially politically motivated. But I don't see how it violates the Constitution, and this falls squarely into the "elections have consequences" category.