under WI state law can a gym club require automatic credit or debit payment withdrawal

Payment method is likely one of the "negotiable" terms in a contract. You do not have to agree to pay by a method proposed by the other side. However, the other side does not have to do business with you if you do not agree. The problem then becomes a question of who wants to do business more?

You are right to be concerned about automatic payments. Sometimes automatic payments become nearly impossible to stop.

Can you and the club come to a compromise? For example, you can pay, in cash, six months or a year in advance. That way the club is certain to get its money and you can keep some information private.

It is legal for the club to do an automatic credit. You are not required by law to give any info but you should do so if you are interested in having your daughter participate in the program. If not, I wouldn't worry about the advance payment requirements.