I personally I dont pay to much attention to gun free signs unless I know that I cant legally carry there because all they can do is ask you to leave. In WA state preemption basically means that cant arrest you for bringing your gun in, but if you do get made they can ask you to leave. If you dont then thats where your going to get busted for trespassing. Anyways, sense I'm not good at explaining things here is the WA RCW on state preemption.
RCW 9.41.290 State preemption.
The state of Washington hereby fully occupies and preempts the entire field of firearms regulation within the
boundaries of the state, including the registration, licensing, possession, purchase, sale, acquisition, transfer,
discharge, and transportation of firearms, or any other element relating to firearms or parts thereof, including
ammunition and reloader components. Cities, towns, and counties or other municipalities may enact only
those laws and ordinances relating to firearms that are specifically authorized by state law, as in RCW
9.41.300, and are consistent with this chapter. Such local ordinances shall have the same penalty as provided
for by state law. 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requirements of state law shall not be enacted and are preempted and repealed, regardless of the nature of the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.