I'm an Everettian...
I'm comfortable with nothing happening in the world besides unitary evolution ...
Measurement isn't something fundamentally different. ...
It seems minimal: you know there's nothing happening but the Schrodinger equation and things are evolving, and if we can reconcile that with what we observe about physics ...
In Ten Years of Quantum Coherence and Decoherence I listed a number of prominent theorists who have expressed some degree of belief in many worlds.
Q1. (largely mathematical): Does the phenomenology of pure state evolution in a closed system (e.g., the universe) reproduce Copenhagen for observers in the system?
This is a question about dynamical evolution: of the system as a whole, and of various interacting subsystems. It's not a philosophical question and, in my opinion, it is what theorists should focus on first. Although complicated, it is still reasonably well-posed from a mathematical perspective, at least as far as foundational physics questions go.
I believe the evidence is strong that the answer to #1 is Yes, although the issue of the Born rule lingers (too complicated to discuss here, but see various papers I have written on the topic, along with other people like Deutsch, Zurek, etc.). It is clear from Weinberg's writing that he and I agree that the answer is Yes, modulo the Born rule.
Define this position to be
Y* := "Yes, possibly modulo Born"
There are some theorists who do not agree with Y* (see the survey results above), but they are mostly people who have not thought it through carefully, in my opinion.
I don't know of any explicit arguments for how Y* fails, and our recent results applying the vN QET strengthen my confidence in Y*.
I believe (based on published remarks or from my personal interactions) that the following theorists have opinions that are Y* or stronger: Schwinger, DeWitt, Wheeler, Deutsch, Hawking, Feynman, Gell-Mann, Zeh, Hartle, Weinberg, Zurek, Guth, Preskill, Page, Cooper (BCS), Coleman, Misner, Arkani-Hamed, etc.
But there is a generational issue, with many older (some now deceased!) theorists being reticent about expressing Y* even if they believe it. This is shifting over time and, for example, a poll of younger string theorists or quantum cosmologists would likely find a strong majority expressing Y*.
[ Social conformity and groupthink are among the obstacles preventing broader understanding of Q1. That is, in part, why I have listed specific high profile individuals as having reached the unconventional but correct view! ]