Legal Question in Employment Law in Washington

Depends on if you have any contract rights with the company.

You seem to imply the employer is forcing you, but I am guessing that is not the case. I am guessing he or she is, at most, threatening to fire you if you do not participate. If you are being forced against your will that would be quite strange indeed.

Generally, you can be fired for any reason or no reason at all unless public policy forbids it (e.g. due to race, religion, national origin, disability, age (sort of), or similar immutable protected characteristic). Refusal to participate in a moral exercise designed to increase productivity (or to amuse the boss) is not generally protected.