What a nightmare for UX are those, I have a experience to share.
On a client product that I was working as UX designer they have implemented the Google Sign Up option, and a huge problem is that by design, the Login button also works as a Sign Up button.
And a common user case was that people initially create their account with email/password, and later in the login page seeing the "Login with Google" button chooses to use it (even if is below the email/password form), and in many cases you got users that create secondary accounts accidentally. Is frequent that people have multiple emails accounts, even Google accounts, you never know.
My client have many support tickets from people mad because they think that his accounts was wiped because was empty.
I try to get the developers find a way to make that the Login With Google button didn't create an account, just check if an account was already created and then login, if not, show a message that an account with this Google account does not exist (like when you put a wrong email in the email/pass form!). But they told me that looking in the Google documentation was not possible (maybe it was).
Now I always try to avoid use third party logins because of that experience.
Of course this is besides the privacy concerns (logged in, Google can track your users) and the dependency problem (if your users Google account is deleted or they lost access, they lost access to the account on your product).