USCIS does not rely on appropriated funding, they rely on user fees (the money YOU paid to file forms). USCIS does not shutdown, the ONLY exception is E-verify which is separately funded. However, where either you or USCIS is reliant upon another agency which is shutdown, delays may be caused. The worst area is employment-based petitions that rely on a labor certification because DOL is shutdown. The FBI probably can continue to process fingerprint and name checks for USCIS because, law enforcement is a TOP priority, USCIS pays for that service, and it is highly automated with few actual FBI employees needed.
Natz Ceremonies, even at a Court, should be OK as USCIS pays fees to the court to fund the ceremonies (pays for facilities and court staff).
