While it looks like there is a variety of successful approaches, I think the reason some have success with one approach and others don't is the nature of the stains. Some stains are simple body oils stuck in the texture of the nonslip pads. Using something alkaline like shampoo should work for those to soften the stains and allow them to be scrubbed lightly. WD-40 should also dissolve those and lift them. Other stains are based on hard water build up of calcium. The calcium can't be seen because it is white but the calcium will catch and hold the body oils. If you cannot get the calcium off, the stains remain. This is where an acidic approach would work. Barkeeper's Friend is oxalic acid with a mild abrasive. If the stains are calcium based, this should wash them away very easily. I would like to suggest another approach to the plain body oils with no calcium build up. There is a cleaner used in the automotive detailing industry called Super Clean. It comes in a purple spray bottle at auto stores, hardware stores, Walmart, etc. It is basically 409 on steroids. If you have trouble breathing when using 409, then you will really have trouble breathing around Super Clean. I bought some for my car and, of course, it works great. Then I read the label and decided to try it in the kitchen. The first thing I tried it on was burned on grease on a stainless pan - the bottom of the pan. I sprayed it on and let it sit for a "dwell time" of 10 minutes. Then I ran hot water from the faucet into the pan and 99% of it just rinsed clean with no scrubbing. I thought maybe I had a pan with grease that looked burned on but was just sort of already softened, but no. I tried it again and again with the same results. So that is my experience with Super Clean. I thought someone might give it a try on their tub texture spots and report back here with results.

Nothing is going to be super attractive, but I have used these translucent treads from Amazon with great success. You just have to follow the alcohol prep process. I've yet to had one peel and have used them in 3 locations, for just the reason you mention -- senior cit mom. ;-) They come in a couple of different sizes, I think, but always get this size. Here is a link that might be useful: Shower Treads

My DD went with the Kohler Archer tub in her remodel. She loves that it is deeper than most tubs so she can soak in it and yet easy to step over for showering. She has been using it for just over 2 years now and the finish is still perfect even with daily well water use. She has the 60x32 K-1123. According to Kohler these are the features: * Comfort Depth® design offers a convenient 19-inch step-over height while retaining the same depth as a standard 21-inch bath. * Molded lumbar support offers extra comfort while bathing. * Slotted overflow allows for deep soaking. * Integral apron. * Integral flange helps prevent water from seeping behind wall and simplifies alcove installation. * Textured bottom surface * Right-hand or left hand drain. One great feature that they don't mention is how many tub toys it can hold all around it.

I've been out of college for, well, a few years, but I'm brushing off my thermodynamics hat for this research For a metal, cast iron has a relatively poor thermal conductivity. That's part of why it's such a good cooking material - it holds the heat you apply. That said, compared to acrylic, it has a significantly higher thermal conductivity. Also, cooking and bathing are different, of course. When cooking, you have the skillet over a heat source. With a bathtub, you add the hot water, and then the heat begins to transfer through the tub and into the room. A cast iron tub has a high thermal mass vs acrylic, so it can hold a lot of heat. I found this website, where they actually did measure it (yay, quantitative data!) and found the cast iron bath water cooled faster than this company's "coreacryl" which is a bit more than just plain acrylic: https://www.bathsofdistinction.com/coreacryl-vs-cast-iron-bathtubs-s/82.htm @artemis78 - with your cast iron tub, do you fill it with really hot water? I'm thinking that if one runs the hot water say at 120F, that would give enough extra heat to get the tub up to temperature, while the water cools to a more comfortable bath temp of say 100-105F. I noticed that link above doesn't show continuous temperature drop. My guess is the cast iron starts to stabilize a bit once the tub temperature and water temperature get more into equilibrium.