Cashiers will need the list_users, create_users and edit_users capabilities to use all the Customer features.
When using WordPress multisite there are some extra checks to prevent non Super Admins from creating and editing customer.
First, in order for non Super Admins to create new customers, please enable the following option in
Network Admin > Settings.
Multisite option to create new users
Additionally, in order for non Super Admins to edit customer details, you will need to add the
manage_network_userscapability to the cashier.