You caught me?
I knew this was a potential problem, and I thought about it, and I never resolved it to my own satisfaction. My inclination is to say that this is on a case-by-case basis. Let me play with a few cases.
Joe believes in an anarch deity, and calls upon that power. He knows, as part of that, that his god is opposed to certain other gods; maybe he realizes that he is on the side of evil, or at least of the rebellion, or maybe he's just in it for the power. Then one day Joe goes toe-to-toe against someone of an alliance faith, and he loses. This shakes his faith, and he decides that it must be because the alliance god has more power than his god. He begins to examine the situation, and determines that he's been serving the wrong god and the wrong side; he's going to go over to the other side.
Now, in this case, an awful lot of Joe's old religion is part of his new religion. He still has a strong faith in the ability of supernatural beings to answer his prayers/spells. He knows something about his new god by contrast with his old god. While his knowledge will be partial, his faith might be greater, since he already believes that this new god has defeated his old god. Further, he has a fair amount of knowledge about spiritual things, in that he knows about the deity who is now his enemy, which is knowledge he can use in his new faith. I'd be inclined to transfer the religion score directly, or penalize it only slightly.
In the alternative, Zack has been a faithful lay follower of an alliance god, moderate amateur religion skill, who has prayed for small things and seen them answered. Then something happens--perhaps one of his prayers fail, perhaps he does something for which he supposes he cannot be forgiven--and he loses all confidence in his ability to call on his god. The player agrees with the referee that he now has not a 1@0 Religion skill but a rather dry 0@1 Theology skill--he believes that there is power, but not that he can access it. Then he needs help, and he still does not believe he can call on his god--but his god has, as you say, enemies, and enemies who would gladly claim an adherent who was on the other side. He dares to call on one of them, and gets an answer. In this case, he has taken the step into a new religion skill, 1@0 Religion in the anarch faith. His theology skill is unchanged, so he preserves what he knows from before (and if the change had not been made before this time, it is made now).
The problem, though, is whether he loses all of his skills in the process. My inclination is to say no (surprise). If I learned to trust one god to guide my sword, and now I'm trusting another god to do the same thing, the skill lies largely in the ability to trust that a god can and will do this; which god it is falls to the religion score.
It may require changing the ritual, and it's likely that I would reduce any expert level skills to 2@10 professional because of that, but a priest who changes his allegiance is still a priest, in my mind, and can still understand the use of power. It may also be that this deity bonuses or penalizes specific skills differently across the board, that is for example, that a particular deity (whether an anarch or someone like Odin) disdains healing spells and so all such spells are penalized. The skill ability level should stay the same, and unless there are changes made to the spell that should change the chance of success, the sit-mods should stay the same.
That's my thinking on it. I've not had it happen, so I've not had to apply it, but that's how I see it going.
--M. J. Young