Can you remove a doctrine from a unit

Yes. It costs Lotus Water, 1 to 5 of it depending on the doctrine's rarity, and Lotus Water is a shop item, so normally that means real money unless you picked some up from an event.

Wait for a doctrine removal event instead. Removal is free while one is running and they come around often, so there is rarely a reason to pay. They get pinged on the CBGG Discord.

See also: what are unit doctrines and treatises and doctrine alchemy.