Rub a small section of the fiberglass door with fine grit sandpaper. If the paint turns powder and rubs off, do this for the entire door until it's paint-free. If the paint gets somewhat gummy, move on to the next step.
Apply a paint stripper to the entire door according to the directions on the paint stripper package. Let the stripper soak in just enough so the paint softens.
Scrape the paint off the door with a putty knife. Work quickly, but carefully to ensure you get the paint off in a timely manner. If the paint stripper sits for too long, it can eat through the fiberglass.
Remove paint in cracks or crevices along the edges with steel wool.
Dip the steel wool in a container of rubbing alcohol. Rub the entire surface of the fiberglass door with the saturated steel wool pad.
Wipe the door clean with a rag. Continue wiping until the rag no longer picks up paint.
Rinse the door with water to remove any possible leftover paint thinner. Let the door air dry for at least two hours before you work with it again.