One might wonder if it is necessary to enable the sign-up option in order to use the Loyalty feature and whether the stamps would be saved to a specific account.
This behavior would depend on the version of the app visited by the user.
The sign-up would be always be enforced for customers visiting through the PWA. This is due to the nature of a Progressive Web App (PWA) and the many different browsers and browsing modes that can be used making it is difficult to maintain loyalty progress for a customer without an account.
In the case of the native versions of the app (Android, iOS), users are not required to sign-up/login in order to collect loyalty stamps; nevertheless, it is strongly recommended to have this option enabled if the loyalty rewards require more than 1 stamp.
One can change this setting at the following path: Build > Sign-up | Log-in > Content > Scroll down to Loyalty Sign-up. For more information visit Configuring The Sign-Up/Login Feature
Finally, note that the stamps are saved to the specific user account when logged in. In case users have not signed up due to it not being required, the stamps are still saved under an anonymous user. One can see the user stamps activity by following the Checking User Activity Data For The Loyalty Feature article.