Thanks for the reply; I will most likely be writing a longer, not-just-a-link post on some aspects of the argument that to my knowledge were not covered on Less Wrong. Namely, the experiments by David Deutsch which can distinguish between EQM and the Copenhagen Interpretation (but require quantum computers to get much, much better before we can test them), as well as arguments brought up by Sean Carroll and Scott Aaronson.
As for your argument, the idea there aren't many worlds requires an extra collapse postulate, so many worlds is the default interpretation of quantum mechanics. The shut-up-and-calculate interpretation is just a refusal to accept any ontology whatsoever.
I could easily turn it around and say;
CI is no more testable than shut-up-and-calculate-only-probabilities-are-real, or than any other interpretation favored by a particular CI opponent, as long as that interpretation makes the exact same predictions as the orthodox QM.
Since MWI and CI are on equal footing in that respect, and MWI has one less postulate, I think CI should be classified as a fringe position and everyone should provisionally accept MWI, unless they are a particularly dead-set on refusing any ontology at all. Of course, once we are capable of putting entire minds into superpositions we can just test it and find out once and for all.
As for your argument, the idea there aren't many worlds requires an extra collapse postulate,
If you have realism about the evolution of state according to the Schroedinger equation, then you need an extra collapse postulate to avoid many worlds.. But you don't have to have realism about state, so there are ways of avoiding many worlds without introducing collapse.
Sean Carroll, physicist and proponent of Everettian Quantum Mechanics, has just posted a new article going over some of the common objections to EQM and why they are false. Of particular interest to us as rationalists:
Very reminiscent of the quantum physics sequence here! I find that this distinction between number of entities and number of postulates is something that I need to remind people of all the time.
META: This is my first post; if I have done anything wrong, or could have done something better, please tell me!