Hmm. There’s a lot of misinformation here.
First of all, if you heard of OpenID, you should know that it’s long deprecated. Almost no one uses OpenID or OpenID 2 anymore. OpenID Connect is spiritually different from its predecessors (it’s basically JWT on top of OAuth2), and trust me, you’ve all used it at some point, even when not dealing with Google/Facebook/Microsoft, without privacy concerns. It and SAML are probably 2 of the most popular single-sign on solutions out there. Often times it’s all done in the background so you aren’t even aware of it.
Secondly, OpenID Connect doesn’t deal with privacy. It’s about authentication (security), how you authenticate to a third party service (for example, macrumors.com) via an identity provider (for example, google). What that identity provider and service does with your information afterwards is not a concern of OpenID Connect. So to say Apple should not follow the spec doesn’t tell you anything about how private your information is.
Third, getting an authentication service spec right is HARD. There are many, many different things to consider, and people figure out new ways to break it all the time. So to truly bullet-proof a protocol like OAuth2 takes many people working in different architectures across different scenarios to figure out all the weaknesses. While I am not the one to claim that Apple can’t do it if it devotes its resources to it, why would it want to? It would be different if OpenID Connect/OAuth2 somehow leaks privacy information, but as I said, it doesn’t deal with privacy, but security. So unless they found a critical security flaw in OpenID Connect/OAuth2 somehow (which would be very irresponsible of Apple to not report it if that’s the case), it makes the most sense to use the same spec so development teams doesn’t have to learn an entirely new spec that doesn’t offer anything new under the sun.
Finally, if you want to avoid anything Google/Facebook sponsored, you need to turn off the internet or something. Most (if not all) modern web services runs on software sponsored by Google/Facebook/Microsoft.