I can disagree with you on everything from the validity of the Bible as a historical document to the demerits of public education, there's no protocol that will make us reach an agreement.

The "consensus" implemented by blockchains is about stating in public and immutable terms what we have previously agreed, to unallow lies about the past: when we do a money transaction, we have both agreed on the terms of that transaction, that is stored. Later even if someone doesn't remember, or try to fake those terms agreed in the past, the blockchain is there to prove otherwise.