Easy Off Fume Free Oven Cleaner in the blue can. Spray it on, wait 15 minutes, the soap scum just wipes right off. It gets your fiberglass shower or tub sparkling clean! I've been using it for about 5 years now.
I'd imagine the finish has been damaged over the years by scrubbing with abrasive scouring powder - that will do it. The surface now may look dingy and dull; nothing you can really do about that without having it resurfaced. Depending on your water composition, any "soap scum" may actually be hard-water calcification. It's extremely hard to scrub off; you'll need to dissolve it. What vinegar is a pretty effective solvent.