This is a clone of issue OCPBUGS-27366. The following is the description of the original issue:
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To support external OIDC on hypershift, but not on self-managed, we need different schemas for the authentication CRD on a default-hypershift versus a default-self-managed.  This requires us to change rendering so that it honors the clusterprofile.

Then we have to update the installer to match, then update hypershift, then update the manifests.