I have used CLR first, paint scraper and razor blade, and an SOS pad. No kidding! Looked new again. Then I used the Magic Eraser on it. This was on real thick hard dirty stuff left from an apartment tenant. There is a product at Walmart called Awesome (dollar stores also sell it) that works well too. The Awesome works especially good on greasy stove hoods and in the refrigerator behind the shelves and drawers where people forget to clean sometime. Crud does build up where we dont think about.
I also run the vent and open windows when using the CLR and other cleaners. Never had a problem with fixtures or tub surrounds or anything using these products.