Kinda fun to see the whole creed take on "flood the whole world with blood dundunduuuun" actually somewhat grounded in gameplay, tho i don't think it's a Gameplay Mechanic Masterfully Entwined WIth Lore By Developers, just a nice coincidence. Or not. Anyway, the point is: you need to desecrate sanctuaries populated by other creeds to raise devotion for Order. On NG, by the time you'll reach their sanctuary, you''ll populate almost every unclaimed one with any other creed. There's a lot of hearts to be expunged in a mildly boring and repetitive fight copypasted for each creed and sanctuary! Okay, done, you start NG+ with this character. Rewards for devotion ranks carry over into NG+, but ranks themselves don't. Most of the sanctuaries in NG+ will be unclaimed, means you have only 6 "home sanctuaries" of another creeds to desecrate on each subsequent NG+ cycle. Or you can abandon the Order, populate the unclaimed sanctuaries with other creed, then re-join Order and desecrate them, but that's entirely pointless, since you'll lost all your devotion rewards from NG.
In conclusion, remember that if you're planning to amass the devotion-rewarded consumables from Order (which is rational, since they're awesome), your only real chance to turn the Island into a bloodbath for non-believers is the cycle that you're joined them on. On subsequent cycles it'll degrade into poking a fancy skull into unclaimed altar over and over again.