To ask if the world is mutable is like asking if money is real or if the colour red is real. Does it make more sense to talk about RGB values or colours? The only reasonable answer is 'it depends'.
It depends on what aspect or properties one is interested in and what lens is best suited to solve problems or which one personally finds most insightful. The world can be modelled as an immutable sequence of state transitions or as a place full of stateful objects, there isn't any clear answer and programmers shouldn't be too literal about what they perceive the problem to look like but rather think about what toolbox is most useful.