Do guests need to sign up for Stripe or Square in order to pay with credit card?

No. If your listing has Stripe or Square connected, then travelers just enter their credit card during checkout. It's no different than booking a property on other platforms.

The same is true if you have PayPal connected: the checkout shows the PayPal buttons and, below them, an “Or pay with card” section where the guest can enter a card directly. A PayPal account of their own is not required.