Yes, you still follow the norms and dictates of the local bishop or conference, but you don't have to! If a decision of the local bishop conflicts with that of Opus Dei, then Opus Dei takes precedent. That after all is what a personal prelature is all about.
And why does Opus Dei "hide its light under a bushel"? Why don't OD priests put "O.D." after their name?
I am fine with people who want to wear spiky chains and so on, but one area in which Opus Dei oversteps the mark is the requirement that its members go to Confession only to an Opus Dei priest. This implies that OD priests have a special power to forgive sins which other priests do do have.