It actually depends what you mean by RNP. If its RNP AR or RNAV (RNP). Big difference.
Any position disagree is always a go around because you cannot be sure what is right and what is wrong, you need to go around and sort that out.
For any sort of downgrade you can continue in some circumstances in others you have to go around, depends on the type of Approach, whether you are on final (below 100ft.), company SOPs etc.