The company behind AnyList, a grocery list app, has decided not to support Sign in with Apple due to concerns over user experience, customer support, and collaboration. They argue that Sign in with Apple introduces several problems, including the potential for unused and unchecked iCloud email addresses and the complications of the 'Hide My Email' feature. The company is also removing Facebook Login from their app, citing similar concerns and a desire to prioritize user privacy. This decision is in response to Apple's new rule requiring many apps to support Sign in with Apple by June 30th.