Yup, the Magic Eraser is abrasive. In addition to taking the protective layer from vinyl, it is pretty easy to rub right through gelcoat. For me it is the last resort for stains on gelcoat.
For the record, Grady mentions in owners manuals that bleach is to be avoided since it can yellow gelcoat, Lots of 'cleaners' contain bleach.
Grady also recommends acetone for cleaning vinyl. It works very well on bolsters and the like and although I had my doubts about using it, it doesn't seem to harm the material.
Acetone also works wonders on plastic rub rails. Wash first and dry and then use the acetone on a clean rag to remove oxidation and crud.
The nice look won't last very long unless a protectorant is used and there are many options, some pretty costly, but one cheap treatment that holds up for several months and is easy to apply is Mop & Glo floor wax
Every season, before winter layup, I remove all the vinyl cushions I can remove ( I leave the bolsters), give then a damp wipe with a mild soap and when dry, apply 303 protectorant. I do the same for vinyl windows.