This is true to the extent that it’s true to say that functional programming requires you to make copies of immutable structures every time something changes, which is to say not at all.

Multithreading is a problem when you have chaotic ownership of writes and updates. There are decades of prior art showing that this is a manageable problem using various strategies, and it’s not helpful to talk in absolutes rather than discussing the relative trade offs.

When your problem domain has changing global state, do you not have synchronization issues - ensuring that stale data is not used, for example - regardless of how you program it? I recall an article making this point, possibly by the same author.