Striipping is definitely protected under the first amendment, but there might be other reasons for the license situation.

I didn't dig into the history of stripper licensing in Washington in any great depth, but I'm reminded of the fact that licensing rules for adult entertainment venues in San Francisco have been proposed by an association of adult entertainment performers in response to exploitative working environments where dancers were being underpaid, subject to harrassment etc., with strip club managers arguing that regular labor laws were inapplicable because dancers were independent contractors rather than employees:: http://www.bayswan.org/eda-sf/lawstoknow.html

A quick google turned up the fact that there have been some big organized crime/prostitution scandals in Washington state in recent years, eg http://en.wikinews.org/wiki/US_federal_agents_raid_strip_clu... which may have influenced the drafting of regulation eg this one from Kent County, WA (which states the legislative purpose up front): http://www.codepublishing.com/wa/kent/html/Kent05/Kent0510.h...

It's not unreasonable to suppose that some pressure for regulation comes from people within the industry as opposed to those who only want to curtail it.