Guideline 4.8 is non-negotiable: any app that offers a third-party login must also offer Sign in with Apple — no exceptions.
What Apple said
“Your app uses a third-party login service (e.g., Google, Facebook) but does not offer Sign in with Apple as an equivalent option. Per App Store Review Guideline 4.8, apps that allow users to log in with a third-party account must also offer Sign in with Apple. Please update your app accordingly.”
Apple requires that if your app lets users sign in with any third-party identity provider — Google, Facebook, Twitter, LinkedIn, etc. — you must also offer Sign in with Apple as an option on the same screen. This applies even if you only offer one third-party option. The Apple button must be at least as prominent as the other login buttons.
While you're at it — Apple also requires these pages for every app.
Fix this rejection, then make sure you're covered on the compliance side too. Apple requires every app to link to a hosted Privacy Policy, Terms of Service, Support page, and Data Deletion page. No link means another rejection — just for a different reason.