on a plastic bath i wouldn't worry too much. it should be protected and i doubt even something like harpic will do any damage to the bath (though it may to your skin if not washed away properly). i'd say make sure you don't use a strong sponge (the ones with the green top) as this may do more damage.
should consider the shampoo/body wash idea. i know it sounds silly but just think it's designed to get the same dirt off of your body no reason it can't in a bath tub. Aldi products i'd be concerned what it is in the bottle. it possibly even says wear gloves when using this products, where as you know with shampoo it's got to be ok to go on your skin.