I use a paste of baking soda and white vinegar. I haven't found anything it hasn't gotten off yet. My brother-in-law had grungy edge of his tub where it meets the tile and tried a lot of things and figured he'd just have to live with it and I suggested the baking soda and vinegar and it got it clean. It also is not toxic.
I live in the South and use white vinegar to get mold off the stucco in some places on the outside of my house where it tends do gravitate. Spray it on, let it sit a bit, rub with a brush and rinse off. My neighbor borrowed some of my vinegar and she replaced it with a new gallon. The one she got is Heinz brand and labeled "Cleaning Vinegar" "cleaning strength". I'd never seen that before and just used the kind you use in making food but bought it by the gallon. She probably got it at either Walmart or Publix. Vinegar works wonders on so many things.