Legal Question in Employment Law in Washington

No, you're not protected by the First Amendment in this matter, but you may have other protections. The First Amendment starts out "Congress shall make no law...", which means that the government cannot restrict what you say (even that is somewhat qualified, for example, by time, place and manner restrictions, such as the prohibition against yelling "fire" in a crowded theater.) A private employer can, depending on the circumstances, make limitations of speech a condition on continued employment. They do it all the time with confidentiality agreements and unilateral restrictions on disclosing trade secrets.

HOWEVER, there is an important exception. The federal laws that were put in place to protect the rights of workers to organize (form unions) specifically protect the rights of workers to discuss their working conditions among themselves. If your remarks are directed to other employees and concern your working conditions (that includes wages, promotions, working hours, benefits, and much more), it is illegal for your employer to try to interfere with that, even if you do not have a union and have no particular intention to get one.

Hope that helps.