Private images as in ACL-based don't exist in the fediverse outside streams, hubzilla, and perhaps Friendica. So I don't think this is a concern on the near term. I believe private images as in OCAP-based (which is the likely direction Meta would go) will be cached under their access tokens so those aren't really a concern either.
That isn't to say there aren't concerns. Any link to any meta/threads resource which isn't a cached image will be fair game. You might want to see if you manually create an ad-blocker rule or if one already exists for threads and all of meta's other properties - and use it on all your devices. That's the only thing that stands a chance of working in this kind of situation.