Washington Ceasefire is misinformed. To sell firearms as a regular business, federal law requires you acquire a Federal Firearms License (FFL). Part of the FFL contract says you cannot sell a handgun to anyone under the age of 21, though you can sell 18-21 year olds long arms. So it is not illegal for an 18 year old to purchase a handgun, but illegal for FFL dealers to sell it. 18 year olds can still purchase from private owners who do not possess an FFL, or have a handgun gifted to them. Becuase there is no federal law or RCW that outlaws the possesion of a handgun to 18 year olds, it is assumed to be legal. Be aware, I am not a lawyer, this is just my personal interpretation of the law.
Also, I suggest reading the FAQs at the top of the Washington page, and the laws themselves, which can be found here http://apps.leg.wa.gov/RCW/default.aspx?cite=9.41