I can replicate this issue local, by right it shouldn't show the public privacy option since you already enabled the lockdown mode in Easysocial, which mean that public user no longer can access any of your Easysocial stream items in public.
Just for your information, I have locked and marked this thread as resolved to avoid confusion in the future. Please start a new thread if you have any other issues in the future so it will be easier for us to manage your inquiries.