You can choose either Square or Stripe if you want to be able to accept credit card payments made by Clients in MassageBook. You cannot connect with both at the same time. You do have the option to disconnect from one and connect to the other at anytime.
However, you can connect with Square for credit card payments made by Clients + Stripe for money transfers only. If you're connected with Square for credit card payments + Stripe for money transfers only, all credit card payments made by Clients will be processed by Square and sent to the bank account associated with your Square account. Stripe for money transfers only is just used to receive funds for an appointment paid for with a MassageBook Gift Card.