At the risk of being annoying with it, this makes it again a bit more complicated than it has to be. A card having a CP score, a PP score, now additionally a conflict score which would only be introduced for BF. Do you really need CP and conflict score to be different things?

Out of curiosity, in which calculations is CP actually factored in? Is it just tournament qualification and conflicts or am I missing something? Maybe there are some hidden calculations relying on it? Either way, it would be more streamlined to adapt the CP score of the BF cards in the interest of simplicity. Otherwise you would have to display the conflict score too and this clutters the UI or you put out a disclaimer for conflicts which may or may not result in more support tickets when the BF cards don't do what they are expected to do, assuming the disclaimer is not read 100% of the time.

Either way, I would consider this implementation detail for the team to decide and as long as the reduction happens it is fine with the proposal.