I use the Magic Eraser every year to clean the steps, buddy seats, the plastic coping, and the water line of my IG vinyl pool and have not had any trouble at all. I find that it works very well and easy to use. Just used it last weekend when I opened the pool!
In my opinion, the fear about mixing with chlorine is not a concern since the amount of chlorine is relatively low. I would probably not dump chlorine straight from the bottle onto it, but normal cleaning in the pool has worked very well for me.
Bruce