The United States are listed as a secular state (ie. it "is or purports to be officially neutral in matters of religion")
Edit: As I research a bit further, I have stumbled upon an interesting counterargument [1] that enumeration of ethnicity and ethnic groups results in "more political discrimination and state-sponsored violence targeting ethnic groups". Perhaps a similar conclusion could be reached about religious census information.
[1] https://www.tandfonline.com/doi/full/10.1080/1369183X.2025.2...