I Sean Carroll podcast on many worlds interpretation

[Michael Price]

That depends on what you mean by "local" and "realist". Measurements having multiple outcomes violates many people's definition of "realist". And having wave functions that entangle spatially separated systems violates at least some people's definition of "local".

Local means the relativistic Lagrangian dynamics are just functions of X and not X, Y etc. QFT fulfils this requirement and as that is all there is to MWI, MWI is local. No non-local FTL collapse.