I think it depends on whether your definition of OOP is that it uses a message-passing style.

Pure functions don't have to mutate anything because they return values which you can store in new variables.

With message passing style, you tell an object to store new data instead of asking it what new data you should store in a new variable.

It's possible to have objects and not mutate them, by making its methods pure functions that happen to live on the inside of the object instead of outside.

But it's not possible to mix message passing style and immutable objects.

I think it depends on whether your definition of OOP is that it uses a message-passing style.

Pure functions don't have to mutate anything because they return values which you can store in new variables.

var brandNewVariable = pureFunction(foo);

With message passing style, you tell an object to store new data instead of asking it what new data you should store in a new variable.

sameOldObject.changeMe(foo);

It's possible to have objects and not mutate them, by making its methods pure functions that happen to live on the inside of the object instead of outside.

var brandNewVariable = nonMutatingObject.askMe(foo);

But it's not possible to mix message passing style and immutable objects.