I have gone both ways with them first putting the moly on, and then removing it by simply tumbling them in walnut for a short period.
I never got overly excited about what little bit might have remained, as it usually wasn't enough to change anything with the loads.
I also have read the this, that, and the other, about shooting moly coated bullets. To be honest with any decent amount of maintenance on your barrel, which should be done in the first place, there is really nothing I have seen personally come of it.
I used it for over 15 years exclusively coating my own 115gr Partitions and running them at 3150fps from my 25-06. The rifle shot awesome groups when it was new and it will still shoot groups like this at 250yds,
(one fouling round after cleaning and two to check the zero)
I also have a 7mm RM which has digested plenty of moly bullets and it will also shoot nice little groups just like this one does. Both barrels have been scoped and show nothing like what some of the pictures and reports I have seen and heard. I guess I must be lucky, or possibly I just clean my barrels...