Hey Luke,
I just wanted to clarify one thing real quick. You mentioned it's authWithOauthProvider that's opening the popup, but actually I think it's the Google SDK (you're probably calling GoogleAuthUtil.getToken() or something, which I assume is triggering the popup). authWithOauthProvider just auths you to Firebase using a token you got through some other means. This means you definitely could implement a webview-based login flow to get the oauth token and then pass that to authWithOauthProvider, though of course that would be inconvenient.
I'm surprised to hear that Apple is rejecting vanilla apps using the Google SDK for login. I'll reach out to some teams internally and see if I can poke the right folks to get some action on that bug. But I don't have much context at this time. :-/
Certainly sounds like an unfortunate situation. Sorry it's affecting you and your app!
-Michael