Our web app (a personal calendar-management tool) offers both Facebook and Google as social login providers. Sometimes a user who originally signed up using a Facebook account tries to log in using their Google account with the same email address. Because my app's users must have a unique email address, currently this case results in an error, e.g. "Please log in using your Facebook account".
Instead, we'd like to enable users to log in with either social provider, so they won't have to remember which social provider they originally used to log in.
What is a good UX workflow to use when a user logs in with the "wrong" social provider? Is there a particular consumer-facing website that does this very well that we could emulate? This UX should help users link that social account to their existing user account without forcing them to learn about how authentication works under the covers and without scaring users about any security issues involved.
BTW, I've informally surveyed a few users and one complaint I've heard a lot is that "link your social account" UX is confusing on many sites (including here on Stack Exchange!). "I just want to log in with whatever account I want to use" is a common refrain. My app's users are relatively non-technical, so the kind of advanced linking that StackExchange uses feels like overkill for our users. So I'm hoping for a more "it just works" flow without introducing bad security issues. I realize this may not be possible, but I figured it's worth asking the experts here.