You should never mutate values that are in the Redux state, ever:

• https://redux.js.org/style-guide/style-guide#do-not-mutate-state

This can and will absolutely cause side effects, including the app potentially not rendering when it needs to.

If this "mutable object" you're referring to is some kind of class instance or similar, that also doesn't belong in the Redux store:

• https://redux.js.org/style-guide/style-guide#do-not-put-non-serializable-values-in-state-or-actions

edit

Per the discussion in comments, here's how I would suggest handling something like this WebGL context thing:

const SomeParentComponent = () => {
  // Use Redux state to decide when we should show this
  const showWebGl = useSelector(state => state.ui.showWebGl);
  // Standard hooks "forceRender" implementation
  const [, forceRender] = useReducer(c => c + 1, 0)
  // Ref to hold the WebGL instance
  const webGlRef = useRef(null);

  useLayoutEffect(() => {
    if (showWebGl) {
      webGlRef.current = magicallyCreateWebGlInstance();
      forceRender(); // have to force a re-render to pass down the ref value
    }
    
    return () => {
      if (webGlRef.current) {
        magicallyDestroyWebGlInstance(webGlRef.current)
      }
    }

  }, [showWebGl])

  return (
    <MyWebGlContext.Provider value={webGlRef.current>
      <RestOfAppGoesHere />
    </MyWebGlContext.Provider>
  )
}

The WebGL instance itself doesn't belong in the store, because it's not state, and it's not serializable. A Redux store shouldn't be used just as a way to hand around arbitrary values, especially if those values aren't plain JS data.

This way, the Redux state still drives whether the WebGL instance is being created, but the instance itself lives entirely in the UI layer and is still accessible to the rest of the component tree.