Is it legal for someone under the age of 18 to sign a gym membership contract by themselves?

In California, someone under the age of 18 can be legally bound by a contract even though the "age of majority" is 18.  Family Code section 6500 & 6700.  The exceptions are that a minor can not enter into a contract to buy/sell real property or personal property not in their immediate possession or control. Family Code 6701.   For those contracts, the underage person can "disaffirm" the contract so long as no goods have changed hands. Family Code 6710.  In your case, I doubt that any substantial goods have changed hands so you should be able to have your son/daughter "cancel" the contract.  They probably won't be able to get any money back unless you are cancelling within a few days of having the contract signed.  Good luck.

It is not illegal, per se.  But someone under the age of eighteen is not capable (with some exceptions) of entering into a contract, thus is cannot be enforced against him.  It is Civil Code Section 1556.  No action need be taken, justtell the gym that the contract cannot be enoforced due to incapability.