It's not too late. Maybe it is for us: but in 100 years, who will really care about a database of uncomfortably-personal details about their dead ancestors? (Sure, DNA will still be an issue, but give that 1000 years and we'll probably have a new MRCA.) If we put a stop to things now (or soon), we can nip this in the bud.
It's probably not too late for us, either. Facial recognition by skull shape is still a concern, but only if the bad guys get up-to-date video of us. Otherwise, all they can do is investigate our historical activity. Other types of data have greater caveats preventing them from being useful long-term, provided we not participate in the illusion that it's "impossible to put the genie back in the bottle".
So what you're suggesting is we do whatever we can to avoid hitting 2 degrees of universal facial recognition precision? Given that the 1.5 degree target is now inevitably impossible.