Consistency with what

Internal consistency of the science as a body of knowledge. "Consistency with the truth" is better expressed by the simple adjective "true".

It's not consensus either. Consistency is a property of a theory (or a set of theories). Consensus is a property of a set of experts.

pushing for consensus or consistency will not tell you which one is wrong

No, but it will provide impetus and motivation to find out which one is wrong.