React : useEffect updates the state, but does not re-render the view

Firstly, your useEffect has a few issues:

Don't reference the ideasArray as a useEffect dependency if you're setting that value inside the useEffect. That will cause infinite loops because when you set the value, the `useEffect gets called again, which sets the value, which calls it again, which sets the value... and so on. If you depend on the previous value to set the new value, pass a setter function to the setIdeasArray function, for example:

useEffect(() => {
  setIdeasArray(oldValue =>
    [...oldValue].sort((a, b) => {
      if (filterActivated === "scoreAsc") {
        return a.score - b.score;
      } else if (filterActivated === "scoreDesc") {
        return b.score - a.score;
      }
    })
  );
}, [filterActivated]);

Notice how I'm also spreading the oldValue into a new array before sorting. This is because Array.sort is not reliably immutable, so in certain situations it will mutate the original data, which we do not want in React.

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If state changes, there is always a re-render. React's render cycle is not the same as the DOM changing, but React will still run the component render cycle if props or state changes.

The issue you're having is due to using the index as a key for each idea. Using indexes as keys is a really bad idea.

The whole point of keys is to allow React to identify items in an array without it having to re-render them, so by using the indexes, what you're essentially saying is that the first item (always index 0) never changes. Yes, your state is re-ordered, but React sees that the keys have not changed order, so it does not change the DOM to match.

Keys need to be related to the item (such as a unique id), so that React can identify that item by something unrelated to "its position within an array".