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Many Worlds is a rather bizarre interpretation.
\1) Even the creator of MWI, Hugh Everett, agreed that wavefunction is relative and wrote a paper on that, but then he also claims there is a "universal" wavefunction. That makes about as much sense as saying there is a "universal velocity" in Galilean relativity. There is never a mathematical justification for how there can possibly be a universal wavefunction. It is just asserted that there is. It does not fall out of QM naturally, a theory which only deals with relative wavefunctions.
This paper shows some technical arguments for the impossibility of a universal wavefunction:
\2) The EPR paper proves that the statistical predictions of QM violate causal locality (although not relativistic locality), and MWI proponents claim they can get around this by assuming that the statistical predictions, given by the Born rule, are just a subjective illusion. But this makes no sense. A subjective illusion still arises somehow, it still needs a physical explanation, and any attempt to give a physical explanation must necessarily reproduce Born rule probabilities, which as Einstein already proved, violate causal locality. Some try to redefine locality to be in terms of relativistic locality (no-communication), but even Copenhagen is local in that sense!
These papers show how interpretations like MWI simply cannot be compatible with causal locality:
\3) MWI proponents also forget that nobody on earth has ever seen a wavefunction. The wavefunction is just a mathematical tool used to predict the behavior of particles with definite values. The Born rule wasn't added for fun. Einstein had lamented at how if you evolve a radioactive atom according to the Schrodinger equation, it never at any point evolves into anything that looks like decay or no-decay. The evolved wavefunction is very different than anything we have actually ever observed, and you only can tie it back to what we observe with the Born rule, which then converts the wavefunction into a probability distribution of decay or no-decay.
If you throw out the Born rule, then you are thus left with a mathematical description of the universe which has no relationship to anything we ever observe or can ever observe. This lecture below explains this problem in more detail: