If you don't want to offer your subscriptions or one-time products as gifts, you can hide the gift option on the checkout page by adding the following code to the bottom of your theme's style.css file:
Navigate to your checkout page and you will no longer see the gift option available at checkout.
This alone does not prevent gift orders. If someone goes to yourstorename.cratejoy.com/subscribe/gift, that marks the order as a gift and automatically populates the "This is a gift" checkbox. Without the gift form, they'll have no way to uncheck the option.
If you still have routes to the gift page, typically built into designs as a "Give a Gift" button or as a link in the footer of your design, you'll want to remove those to prevent any additional orders as gifts.
Related links: How Does Gifting 2.0 Work?