If you go to https://myaccount.google.com/permissions https://myaccount.google.com/permissions, you can turn off "Google Account sign-in prompts" on each of you

If you go to https://myaccount.google.com/permissions https://myaccount.google.com/permissions, you can turn off "Google Account sign-in prompts" on each of your Google Accounts and then you won't see any more of those prompts. Don't know if Facebook has a similar option for their accounts though; I've seen a similar sign-in prompt elsewhere for Facebook.