By default, when adding a contact to a list using opt-in forms, mass upload, API or third-party integration, you have to provide an email address with the contact which is the primary identifier of that contact. To override this setting and allow adding contacts without an email (ex: Contact us form on your website), navigate to your Lists page and from the right side options drop-down choose Fields & Form. Expand the Email Address field and mark it Not Required.
Note: This setting can impact the performance of your automation.