That would be Naturalized Citizen not Nationalized.
Naturalization papers do not give a specific date, they will read that the prospective Citizen arrived "on or about such and such a date" So your search is much too narrow.Also it is not uncommon for the wrong ship and port of entry to be incorrect, after all Charles would have been age 16 or less, so he simply may have been mistaken.And in those years there was no verification of entry into the US when one was Naturalized.
Doing a search allowing a variation of +/- 2 years for the birthdate and 5 years for year of arrival finds
Name: Carl Rehfeldt Arrival Date: 18 Nov 1856 Birth Date: abt 1841 Age: 15 Gender: Male Nationality: German Place of Origin: Mecklenburg Port of Departure: Hamburg, Germany Destination: United States of America Port of Arrival: New York Port Arrival State: New York Port Arrival Country: United States Ship Name: N Coopelk Accpmpanied by Johann age 50 Johanna age 51 Wife Johanna age 18 Daughter Maria age 15 Daughter Carl age 14 Son
The following couple are found in the 1880 Newton, Manitowoc, Wisconsincensus John REHFELDT age 76 Jane REHFELDT age 74 Living next door are Chas REHFELDT age 31 with wife Charlotte and 7 children