Facebook would work perfectly fine with fake data and without privacy violations.
I can sign up with a fake date of birth and a throwaway email account, under a generic name (remove any identifying unique spelling or middle names, for instance) or a completely fake name. And I could still connect with friends and family, provided I know the names they've chosen to use on FB.
According to the GDPR, anything you share publicly is basically fair game. So if you post something in a public post on your public wall, anyone can view and use that data for whatever they want.
The issue is all of the secret data FB collects. They have disturbingly extensive profiles of every one of their users, including political standpoint, which phase of life they're in (eg. "stable established adult" or somesuch), their sexual preferences, sports teams, club memberships, medical history, the list goes on and on. They get this from your non-public account information and from tracking you across websites you visit.
That is the issue here, the tracking and storage of personal information that people want to keep private. FB's tracking and privacy violations are not vital to the service they provide. Their business model may depend on (targeted) ads and privacy violations, but that is not an excuse. You cannot base your business model on breaking laws and hoping to get away with it.
FB isn't "allowing" users to either agree to the ToS or go pound sand, they're basically saying "fuck you, we'll exploit your private information as much as we want, and you don't have a choice". They're doing this to muddy the waters and make people think "oh I already agreed to this, make it go away", when the actual GDPR consent form pops up after the 25th.
But users do have a choice. The GDPR very specifically says that you cannot make access to your service contingent on opting in to private data collection and tracking, because consent has to be given freely, ie. not under threat of access denial.
You can only do this if your service cannot possibly work without the collection of personal data. Something like Strava (which tracks bike rides via GPS) cannot function without collecting GPS locations. So they have a good argument that they cannot provide their service, if users do not opt in to location tracking. But they have to very clearly state what they will use this collected data for, and they cannot change it later without collecting new freely given consent from their users.