I tore out my metal framed shower door.
My lousy dimpled glass shower doors were attached with aluminum trim on the front ceramic tile walls, and the screw holes might be easily patched with white tile grout.
Then the spots are visible.
Tile grout will not work with a fiberglass shower. There are patching compounds, such as Bondo, made for boat and auto repairs that could be used to make a waterproof, permanent seal for the screw holes.
Or these plugs might do you well:
I ended up using the little buggers, fairly successfully.
Whether you can "realistically" do a good job depends on a number of factors.
If the fiberglass shower walls are not the exact same white as the dried epoxy patch or Bondo, matching the patch may be impossible.
If you want the old screw holes to be completely invisible, your best bet might be to hire a bath refinishing company to patch and resurface the whole shower.
A cheap (IE $5) solution is replacing the screws holding the shower door trim with slightly longer, ovalhead, stainless steel screws, each with a small rubber grommet (washer) to seal the hole.
This is one of those times when a trip to a local hardware store and a discussion with people who know the difference between ovalhead, roundhead and flathead screws about what you are trying to do will produce an inexpensive, simple and permanent fix for the screw holes.
Take along one of the old screws to make sure the replacement screws are long enough to fill the old screw holes and are about the same diameter so that you do not crack the fiberglass with a "fatter" screw. Yup, my wallet holds a lot of screws. I don't think there is any change in there...just screws.
A number of slightly off-color patches would bother me as much as my inability to clean my old glass shower doors, which drove me to rip them out.
But if you don't mind the color and condition of your current shower stall, redoing the whole thing redone to cover a handful of screw holes seems a bit excessive.