The Super Puma fire drill is the obvious example. According to RFM when the fire warning comes on you pull the big red handle, the engine stops.
That would be fine if the ratio of spurious fire warnings to real ones wasn't over 1000:1. If we followed the RFM we would spend most of our lives on 1 engine.
Of course the solution is to improve the fire detection reliability but whilst EC/AH have been tinkering with it ever since it came out in 1982(?) and it has improved, it is still very unreliable.
So we had a completely different EOP for fire for many years, that was more cautious about shutting down the engine and taking a few moments to try to verify that it was actually on fire (which it virtually never was).
Of course EC/AH didn't want to change the RFM since that would be an admission of the lack of "fit for purpose" of the warning system, and anyway the heat was off them as our procedures worked well. Before I retired in 2013 I was aware that another operator had been forced by CAA to implement the RFM procedure which was a shame. Whether that has now been imposed on us I don't know, but it would be a shame to throw away decades of experience in favour of a manufacturer's procedure coloured by vested interest.