Is my customer payment data secure?

Autoship uses the  WooCommerce Payment Token API to securely store payment methods that your customers use to make purchases from your store.  This ensures that the liability for payment security is with your payment gateway provider and not your store or website.

Here's an excerpt from WooCommerce explaining Payment:

Payment tokens in WooCommerce allow you to save the tokens/keys you use for communicating with various payment processors. They also store the other meta information needed to process a payment. For example, credit card tokens store the four digits of a card, the card brand/type, and expiration information. eChecks store their last four digits. New types of tokens can be easily built and used with WooCommerce.

Read more about Payment Tokens from the  original post by WooCommerce