Reddit states in the privacy policy that they are already sharing this information already:

How We Share Information

Much of the information on the Services is public and accessible to everyone, even without an account. By using the Services, you are directing us to share this information publicly and freely.

When you submit content (including a post, comment, or chat message) to a public part of the Services, any visitors to and users of our Services will be able to see that content, the username associated with the content, and the date and time you originally submitted the content. Reddit allows other sites to embed public Reddit content via our embed tools. Reddit also allows third parties to access public Reddit content via the Reddit API and other similar technologies.