The way I see it working would be that they gain the points from indulging in behaviours that theybwere taught were wrong but deceived into thinking (possibly out of pride) that they may now freely indulge in, and the "false faith but really confidence" points would reinforce this reasoning.
God wants you, Billal bin Mehmet, to drink wine. If not, why do you feel so good after a drink with your friends.
My preference would be to use a Delusion flaw and some other way of replicating True Faith's advantages (e.g. Magic Resistance), rather than simply a False Power: True Faith. I would be more open to granting False Powers like Sense Holiness and Unholiness, Second Sight. I could see an infernal Ars Notoria tweaked with an Accuser as a replacement Patron Angel and False Powers for Sense Holiness and Unholiness that give the type of information the demon wants the faithful to get. I suppose some False powers with the methods and powers of the RoP:D could be fitting in some instances. Invocation + Cursing, maybe
But then, how is this different from the Christianity X Judaism X Islam dilemma? I mean, my personal view of that in the setting is that all of the three are sufficiently right to receive approval, but none is entirely right.
If you character with False Faith receives God's approval isn't this True Faith in the end, even if he doesn't follow the standard doctrine of his faith?
Where do you see this falling in the spectrum? Good, but incomplete, possibly a bit misguided? If so, I'd say this is True Faith. Completely misguided, but delusional, thinking it's actually good? I really can't see the divine supporting that in the same way that it would support the "correct" path.
To me the False Faith would be the negative stereotype of a televangelist, but les cynical. They believe the have THE TRUTH about religion, that they have been chosen to lead the masses, to save the chosen people, etc. There is no humility, and their service to the divine is simply service to themselves, and they may have trouble seeing space between the two. Anyone who argues with them is arguing with God, and the glorify God to glorify themselves.
It is somewhat trickier than the false Gift because the Gift doesn't have a moral dimension, and of course the infernal is always wondering why God has allowed this false Gift to exist and if they aren't somehow being tricked themselves...
Why would such characters / NPCs even need Faith points, miracles or any equivalent of True Faith? In a saga such people work well as just political figures of different influence.
Giving them supernatural substance and powers of any kind derived from their bigotry just needlessly complicates a saga. If required in a story, they can just hold an ArM5 p.48 Relic.
The way I see it the false faith points comes from engaging in behaviours that the falsely faithful person sees as virtuous, but which are in fact sinful.
As an example a bloodthirsty inquisitor-type who believes that they are doing gods work by persecuting people to an extreme degree for the slightest sins would gain false faith points whenever they commit such persecutions.
They would do so because they perceive the persecutions as necessary to remove and punish sinners, but in fact it is way over the line for what is necessary and acceptable within the tenets of their faith. Thus they falsely perceive a sinful behaviour as virtuous.
So our Konrad of Marburg might have both Faith points for a pilgrimage, and False Faith points for rigging inquisitorial proceedings netting him a most severe Papal reprimand: "Talem miseriam, ut nobis dixistis, non permittimus!". Right?
And the SG keeps these separate or accounts them against each other? Very tricky and complicated! And for which purpose?
So long as he is an NPC, I don't think that I would give myself a headache over it: he'd not have the faith point (possibly having spent it impiously and had his old true faith virtue replaced by false faith), merely the false faith ones, which he regenerates by torturing people.
If somehow, the party were to befriend him and manage to recruit him (maybe staging his death and inviting him to come to their covenant), then i would stat him from scratch with false faith.
In theory yes. But like @Jank I wouldnt bother too much with it until it became necessary for him to have stats like that.
or possibly his pilgrimage faith points didnt exist since the divine decided not to reward him with faith points when he is unwittingly serving the infernal by his action.
or any number of other I needed to resolve this dilemma in order to tell a story I would leave it be, and not worry too much about the somewhat paradoxical situation of someone having both infernal faith points and divine faith points.
By a certain interpretation it isn't over the top. if someone's behaviour is sinful and will result in an eternity of suffering, no mortal suffering inflicted upon them is too severe, if it brings them back to confession and God's graces.
There are many ways to make a false faith work. Nearly any behaviour can be interpreted in interesting ways to make it look virtuous or sinful.