Consistent Histories is usually presented as a Copenhagen style interpretation, explicitly so in the books of Griffiths and Omnès. Also in both it and QBism the Moon is there when nobody looks.
I'd say at the Moon question QBism, Statistical Ensemble, Consistent Histories and Neo-Copenhagen views (e.g. Bub, Healey, Brukner) all branch off from Relational. You'd then need a set of precise questions to separate them.
I think the first one to ask would be:
"Do Probability 1 events represent a sure occurrence?" or something similar like
"Given a set of experimental conditions is there a single rational probability assignment?" or even more briefly
"Are you a Subjective Bayesian?". That would separate QBism from the others, with QBism being a "No" answer.
EDIT: I actually think
"Are experimental outcomes objective facts?" is a better selector for QBism
After that a similar question asking whether you hold a Frequentist view of probability will pull out the Statistical Ensemble view.
Finally
"Can Classical Mechanics be derived from QM?" with
"No" giving Neo-Copenhagen and "Yes" giving Consistent Histories.
I'm still holding out for my
"I wish I could shut up and calculate" interpretation swinging the hearts of the physics community.
