When credit card information is entered within your MassageBook account while enrolling a client into a membership, the information is stored within your Square or Stripe account.
If you have active memberships in your MassageBook account and disconnect from Square or Stripe, no changes will occur to the memberships at that time as they will all remain active. However, if you do not reconnect to the same Square or Stripe account before a membership attempts to renew, the renewal will fail as there is no longer a link to process the card.
Issues can occur though if you switch between processors while you have memberships active. For example, if you are connected to Stripe, enter all your membership information, then disconnect from Stripe and connect to Square, MassageBook will no longer have access to that credit card information and renewals will fail. The client's card information will need to be re-entered into MassageBook so it saves within the new processor.