If it says RNP-1, then that is the requirement. If the airplane is certified and crew are trained for RNP-1, and your Op Specs allow RNP-1 operations, then you can fly the procedure. If ANY of the above 3 requirements is missing, you are NOT allowed to fly the procedure.
If there is an exception, e.g., "GNSS required", then it will be explicitly stated on the procedure chart.