While not related to immigration necessarily, we do have a question when doing face to face census counting (we = I am working as a Census enumerator temporarily) that calls out Hispanics specifically, and frankly, is a bit uncomfortable.
So you get the name, confirm address, ask how many people lived there on April 1, and then a separate screen comes up that specifically asks (everyone) if they are of Hispanic or Latino origin. If yes, then from where exactly. I do wonder why that question is in there, by itself. There may well be a legitimate counting purpose in asking, but if I were illegal, 1. I wouldn't be opening the door to anyone knocking and 2. I sure as hell would not answer that question. And I believe there is a different branch of questioning that comes up if they answer "yes" as well.
Then you ask the question (again, of everyone) what their race is, and within that question, is a statement (that we must read) that says "For the purpose of this interview, Hispanic is not considered a race" So if they ARE Hispanic, they have to choose: white, black, Pacific Islander, Native American, etc. This question ALWAYS stumps people that answered "yes" to the Hispanic question (which makes sense to me). One smart guy I interviewed (who obviously was hispanic, and specifically from Mexico), answered "Native American".
And if you do that, then it asks "Which tribe?" And so on...guy just kept making up answers all the way down.