If Apple is perfectly happy with other sign on, then privacy is certainly off the table. Otherwise, they wouldn't allow apps in their store offering any other sign on (extreme analogy would be apps with virus in it). Then why force developers to add Apple sign on even they don't want to, instead of just encouraging? They can easily do so by telling developers that "apps with no Apple sign on are allowed, but are placed low priority queue so the review process will take longer".
It is pretty standard "embrace, extend, and extinguish" strategy. Similar to what's happening in the browser market. They are waiting for majority of the apps to have their sign on and majority of users use Apple sign on, then update the policy to disallow other methods.
I mean I don't have any issue of Apple doing these in their own ecosystem, but at least don't be so hypocritical or naive when defending them.