Priest of Old Wyk says it contributes its STR to your total for dominance. Traitor to the Crown says it does not. Which card effect wins? We know that "cannot" trumps "can" because RRG says "cannot is absolute", but neither of these cards says "cannot", and there doesn't seem to be any general rule about restrictions trumping permissions...
Priest of Old Wyk
While there is a Drowned God character in your dead pile, Priest of Old Wyk contributes its STR to your total for dominance even while kneeling.
Traitor to the Crown
Attached character does not contribute its STR to challenges or to its controller's total for dominance.