Spray the vinyl siding thoroughly with a hose. This will remove any loose poop from the siding as well as wash away any spider nests.
Add a decent amount of lacquer thinner to a rag and begin to wipe down the spider stains. The chemicals that make up the lacquer thinner will break through the spider poop, removing it from the siding with a few wipes.
Use a ladder to reach any spider stains that are high on the siding.
Spray the vinyl siding with the hose to wash off any leftover spider poop and lacquer thinner.