There is another method to stop Skype from starting.
Next time when you start your Mac, you should not see Skype automatically starting. 537 for Skype for Business Server 2015, Web Components Server. Right click on Skype icon in the Dock while holding Ctrl key. To fix this issue, install the January 2019 cumulative update. After you apply this update, the mobility policy is applied only to the mobile clients. The issue occurs because the mobility policy was applied to the Skype for Business on Mac desktop client, and it was by design. It's expected that the Skype for Business on Mac desktop client can save the sign-in credentials. However, when a user tries to sign in to Skype for Business by using the Skype for Business on Mac desktop client, the password is also not saved even if the user selects the Keep me signed in option on the client. In this scenario, users can't save their credentials information (such as passwords) on their mobile devices. In a Microsoft Skype for Business Server 2015 environment, you create a Skype for Business mobility policy in which the AllowSaveCredentials parameter is set to False.