React useEffect causing: Can't perform a React state update on an unmounted component

Sharing the AbortController between the fetch() requests is the right approach.
When any of the Promises are aborted, Promise.all() will reject with AbortError:

function Component(props) {
  const [fetched, setFetched] = React.useState(false);
  React.useEffect(() => {
    const ac = new AbortController();
    Promise.all([
      fetch('http://placekitten.com/1000/1000', {signal: ac.signal}),
      fetch('http://placekitten.com/2000/2000', {signal: ac.signal})
    ]).then(() => setFetched(true))
      .catch(ex => console.error(ex));
    return () => ac.abort(); // Abort both fetches on unmount
  }, []);
  return fetched;
}
const main = document.querySelector('main');
ReactDOM.render(React.createElement(Component), main);
setTimeout(() => ReactDOM.unmountComponentAtNode(main), 1); // Unmount after 1ms

<script src="//cdnjs.cloudflare.com/ajax/libs/react/16.8.3/umd/react.development.js"></script>
<script src="//cdnjs.cloudflare.com/ajax/libs/react-dom/16.8.3/umd/react-dom.development.js"></script>
<main></main>

You can try this set a state like this and check if your component mounted or not. This way you are sure that if your component is unmounted you are not trying to fetch something.

const [didMount, setDidMount] = useState(false); 

useEffect(() => {
   setDidMount(true);
   return () => setDidMount(false);
}, [])

if(!didMount) {
  return null;
}

return (
    <ArtistProfileContainer>
      <AlbumContainer>
        {artistData ? artistData.artistAlbums.items.map(album => {
          return (
            <AlbumTag
              image={album.images[0].url}
              name={album.name}
              artists={album.artists}
              key={album.id}
            />
          )
        })
        : null}
      </AlbumContainer>
    </ArtistProfileContainer>
  )

Hope this will help you.

For me, clean the state in the unmount of the component helped.

 const [state, setState] = useState({});

useEffect(() => {
    myFunction();
    return () => {
      setState({}); // This worked for me
    };
}, []);

const myFunction = () => {
    setState({
        name: 'Jhon',
        surname: 'Doe',
    })
}