It is not true that "any mutation" causes issues. In fact, most idiomatic usage of mutation is problem-free and completely sound.
One can find out more about polymorphic mutation as a "counterexample" to Hindley-Milner type inference on Wikipedia [1]. It's a well-studied problem with space of solutions. Purity, weak references, the value restriction, etc. are all ways of dealing with this shortcoming of Hindley-Milner.
Interestingly, one of the first proposed solutions to this problem was suggested by Wright in the journal "LISP and Symbolic Computation" [2].
