My name is Dallas, I'm from the Social Care Team here at Shopify!
Accepting returns is definitely not mandatory, by any means. However, having a refund policy on the page is still recommended. This way the terms are clearly laid out for the customer and it helps to prevent any future confusion or questions that may arise in regards to a return. With a return policy clearly laid out then there is no room for potential frustrations.
With that being said, that doesn't mean that you have to _accept_ returns. You can have a return policy, but have it state that refunds are not available.
This great blog post gives 9 Tips on Creating an E-commerce Return Policy, and even states that sometimes that would mean not recognizing refunds.
I hope that's helped! Please feel free to let me know, and you can always give us a call or start a live chat at any time. We're open 24/7 for your convenience and always happy to assist!