I would avoid anything highly acidic, or high alkalinity come to that
Toilet cleaner like harpic can work miracles, but it will damage aluminium , and even chrome taps....
I have a hansgrohe sink tap, I put some harpic at back of tap to remove a bit of stubborn limescale.....left 10 mins as was distracted, it's leached in to the chrome plating.
So in domestic jobs I would just use limelite and non scratch scourer, after a few cleans it will improve,just tell custy it takes a whole to get the screens nice.
Also, most shower screens have aluminium frames, even limelite will mark these if left unatttended.
Mr B