Under current state law, the state of emergency does not clearly change anything. The health club contract law is here: the crucial thing is, you have to read the contract. The law did not anticipate a governmentally-mandated shutdown, but does address the question of cancellations in RCW 19.142.040(7). The two most-relevant conditions are:
(c) If a contract extends for more than one year, the buyer may cancel
the contract for any reason upon thirty days' written notice to the
(d) If the health studio facilities are permanently closed and
comparable facilities owned and operated by the seller are not made
available within a ten-mile radius of the closed facility;
But, I assume neither is actually applicable (membership is not longer than a year, the closure is not permanent). (8) also requires "Clauses explaining the buyer's right to a refund and relief from future payment obligations after cancellation of the contract" (that is, they have to say what your rights are).
There is nothing illegal about a contract clause that says something like "If the facility is temporarily shut down due to circumstances beyond our control, we will extend your membership (obligation) by the duration of the shut-down". As a general matter of contract law, one party cannot unilaterally modify the term of a contract, unless there is a clause that permits them to do so. State law requires that the contract have a stated duration. So one argument that you could make is that without an escape clause in the contract, they are in government-mandated breech of contract. (But it is highly likely that there is some such clause in the contract). The crucial legal question is, what gives you the right to cancel the contract? If you have such a right, then the law also states the pro-rata refund requirements.