I know that legal arguments can sometimes be confusing, but it is a bit surprising to see the City of Olympia do a complete 180 in just two short years concerning its authority to impose a local income tax. Consider the following positions the City of Olympia has taken: 

• 2016 - Olympia files a lawsuit to stop a local income tax from being on the ballot saying: 
   
  • "The proposed Income Tax Initiative clearly conflicts with state law."
     
  • "The proposed Income Tax conflicts with state law which prohibits local governments from taxing net income."
     
  • "Because the proposed Income Tax Initiative seeks to levy a local tax on net income, the proposed Income Tax Initiative clearly and unambiguously conflicts with Washington state law."
     
  • "The proposed Income Tax Initiative conflicts with RCW 36.65.030, which prohibits local governments from levying a tax on net income."
     
• 2018 - Olympia joins AWC amicus claiming cities have broad authority to impose income taxes. 

I'm tempted to file a public records request to see what possibly could have changed for Olympia in the last two years, but I'm pretty sure it would be denied claiming "attorney client privilege." 

I think Olympia got it right in 2016. In fact, King County Superior Court Judge Ruhl would probably agree since he ruled the Seattle income tax illegal saying: 

"To summarize, the Defendants’ motions will be denied and the Plaintiffs’ motions will be granted because the City’s tax is not an 'excise tax' and thus is not authorized by RCW 35A.82.020 and RCW 35.22.280(32); the City’s tax is not authorized by RCW 35A.11.020; the City’s tax is not otherwise authorized by any other statute; and RCW 36.65.030 prohibits the tax."

Additional Information
Olympia Council can help Seattle Council understand local income tax ban
AWC argues every WA city should be able to impose an income tax
Timeless advice from WA Supreme Court on income taxes