I clean my tubs weekly using Lysol bathroom spray (aerosol usually, though the trigger spray version is good, too). If/when the no-slip circles happen to look a little grimy, I’ll gently rub a damp magic eraser over them.

Usually the weekly cleanings keep them looking good. We don’t walk around barefoot much, so they don't tend to look bad very often if at all.

i have a non skid tub that is about 12 years old. Doesn't get used vry often, but the bottom looks fine. One cleaning person apologized because she scrubbed and scrubbed and the bottom still felt gritty. Go figure!!

Some cleaners don’t work. I was actually using shampoo for a while with a scrub brush. But then I switched to a fiberglass boat cleaner. It requires less scrubbing.

Oops, I should add that I never had cast iron.

This is a very old thread, but the suggestion of Dawn works well when regular cleaning doesn't get rid of the "stains." The stains are generally oils from shampoos, soaps, and body oils. Dawn does the trick. When the non-slip surface in our cast iron tubs start to look a bit grimy, I add some Dawn, a bit of water, and maybe some bleach to the tub. I then let it sit for a few hours or overnight.

It seems to be a theme for me here lately, but I'll say it again. Don't use magic erasers on a surface you don't want to scratch. I'd never use one in a tub.

I forgot to include the link to the old thread.