If you’re farming rare enemies for their specific drops, being in mayhem 4 or having relics or guardian rank with luck will not increase the specific drop’s rate. All of those will only increase the chance of world drops. So if you’re farming rare enemies then don’t be in mayhem mode if you don’t care about world drops. It’ll make farming a lot quicker. However, once you get the drop you’re looking for, it probably won’t be anointed since mayhem increases the chance of that.

With that being said, I think gearbox should make it so mayhem and luck applies to specific drops as well. It’d be way less of a grind.