The answer to this question depends on how you define OOP and FP. I think the answer is "sort of".

The problem with OOP is that it encourages the proliferation of mutable state. If each object has mutable state, then a large object-oriented program has distributed mutable state, potentially in hundreds of different silos. Problems like concurrency become impossible to reason about.

FP encourages the careful sequestration of mutable state. It's false to say that FP outlaws it entirely, since it's hard to do anything useful without side effects. However, functional style limits and sequesters mutable state to such a degree that it's usually easy to reason about what side effects are happening.