Same. We momentarily considered adding Apple Login to our app when they changed the rules a couple weeks back, but instead we are removing all social login and migrating all accounts to (email/username)/password. Why?
Because a) it's even more code we now have to support, both in our apps even on android and on web -- a huge investment we are not prepared to make, and b) because for what we do, we actually do need to know the user is who they say they are (we offer the ability to contract a service between third parties, which means anonymity is NOT desired). I was never really comfortable using social login at all, for that second reason, but was pressed to by my peers; after Apple's shenanigans we came to the mutual decision that it was time to cut the cord. The login screen is already busy enough, we don't need yet another button. So we'll simplify.
For this latest change, it won't affect us much because I have always made it a policy neither to trust, nor to rely on, the data in Local Storage, and only to use it for performance boosting via caching. If data isn't there, it isn't there, and we go get it. This is largely due to historical reasons where browsers have always borked the LS implementation in one way or another, but it's beneficial now in that it won't really change anything for us.
I do feel for folks that are using it for genuine storage though, I know some apps that use it in order to AVOID storing private data on their servers, which will now have problems and be forced to reduce privacy in order to adapt.
This is definitely a power play on Apple's part to further weaken the web ecosystem. Device sales have been falling for years, they know their cash cow is their 30% cut on app purchases and IAP, and they aren't going to let the browser cut into that. Any "privacy" benefit in this case is purely incidental (and as noted above I believe it will do the opposite in many cases).