Blockchains as commonly deployed seem to be more AP to me: you can get into split-brain and while there's a way to select the canonical form after the partition is healed, that's after the fact. Whereas e.g. Paxos won't even let you do anything without knowing it has quorum.
alas, because blockchains allow open participation, there is no reliable definition of split-brain, or network membership, or anything at all, really
because there is no canonical definition of the set of nodes which represent a source of truth for the state of the blockchain
the blockchain state is a function of game theoretical (read: unreliable and non-deterministic) algorithms that assume the result provided a majority (typically 2/3) of participating nodes can be assumed to be valid
they are I guess CP based on these assumptions (and others), but those assumptions are probabilistic, they absolutely can be violated, and those violations create forks of the chain which invalidate even the weakest consistency models
and nobody seems to care
the notion that blockchains are "trustless" is a complete fiction, all state necessarily exists in the context of some trusted authority, decentralization just means that this authority is not well defined, arbitrary from the perspective of its downstream consumers, unaccountable
Yeah, I should probably say "they're treated as CP systems", in that they purport CP guarantees, when in reality they adhere to almost none of them (but, they also adhere to none of the traditional expectations of an AP system, i.e., a way to heal partitions and restore some form of consistency).
