It's not a (provable, guaranteed) CP system. Bitcoin attempts to provide a global consensus across a large number of actors, but its attempt is based on proof of work, specifically that it's probably difficult to compute hashes with a certain property (leading zeros, last I checked). It in no way guarantees consistency in the face of partitions.

Consider the simplest case: 1/2 of bitcoin users/miners are temporarily split off from the other half, for say a week (all atlantic/pacific fibers are broken at once, all satellites fall out of the sky, other huge catastrophes occur all simultaneously). Each half would append their own blocks to the blockchain happily, and depending on the chain lengths added, once the partition went away there would be no good way to reconcile. Thus: not consistent in the face of partitions.