At some point you need to break the paradigm to do anything useful, be it some IO, or whatever. Working in a FP way for as long as appropriate will make large parts of your program better testable and avoid large amounts of unwelcome surprises. If at some point you got some result, which you want to let affect the real world, then you can still limit mutation to that place, where you got the result. I would avoid that for as long as possible, to have larger parts of my program be easy to reason about.

GUI has been one of the strongholds of mutation-encouraging paradigms though. It should be said. I would use it as an example, where one probably might need mutation for performance reason and for the reason, that I find it a bit too overheady to create a new widget for every small change. I don't know enough about how some languages try to solve this and stay declarative or functional, to comment on that.

this is me being cheeky, but how do you know that the real world is mutable?

if you believe in super-determinism and that everything progresses based on predetermined laws you can take the view that space+time already exists in all its past and future and that nothing happens.

or, quantum mechanics in the multiple world interpretations. you can say that the state of the world literally splits whenever there is an event.

i guess the metapoint here is that just because something seems mutable does not mean it’s really mutable and that mutable and immutable only make sense at certain levels of matter organization (are atoms mutable? what about photons? what about quarks?)