And I disagree with rapgood, as it is his interpretation of the court's opinion on Sequim.
The RCW 9.41.290 clearly states "Local laws and ordinances that are inconsistent with, more restrictive than, or exceed the requirements of state law shall not be enacted and are preempted and repealed, regardless of the nature of the code, charter, or home rule status of such city, town, county, or municipality."
RCW 9.41.280 clearly states firearms are not permitted on public or private school premises. There are not broad state laws prohibiting firearms from parks, city buildings, convention centers, halls, etc. Additionally, the Sequim case specifically addressed the municipalities' power; not school districts', which are their own entity. Important, since 9.41.290 does not identify school districts as something subject to that particular RCW.
In a better world, I don't believe .280 should extend past school hours (rather not have the law at all). Prohibiting firearms on school property when school is not in session is idiotic. But hey, if someone wants to be the guinea pig case for this, go right ahead.
Don't forget, once you're done with WA law, you have the Federal law to contend with.