If I enchant my opponent's creature with Alpha Authority, which gives it hexproof, can its controller target that creature with a Mutate ability?
They can. Hexproof means "This permanent can't be the target of spells or abilities your opponents control" - and as it is the creature that gets Hexproof, then the "you" means the creature's controller, not Authority's controller. So you can't target that creature anymore, while your opponent still can, with Mutate or any other kind of spell or ability.
They can. Hexproof means "This permanent can't be the target of spells or abilities your opponents control" - and as it is the creature that gets Hexproof, then the "you" means the creature's controller, not Authority's controller. So you can't target that creature anymore, while your opponent still can, with Mutate or any other kind of spell or ability.