There are two separate things here.
1. Father not named in birth registration. This is an issue of legitimacy, that is, his parents were not married. I have seen other German civil records around this time period that indicated parents were Jewish. In fact, there have been some posted on WikiTree where people have asked for translation help. While anti-semitism did exist at this time, the really ugly aspects, ie, the Holocaust, came later.
2. US citizenship. In the census records, unless there is other information, a person in the census was considered a citizen, and this would be indicated by his/her stated place of birth (a US state or territory). If was person was an immigrant, the year of immigration would be given. If the person had become a naturalized citizen, the record would be annotated “N” in the appropriate field, and in some censuses the year of naturalization. If the person had not yet become a citizen, the records would be annotated “A” for alien.