From what I remember, you had access to the data that would be visible to a users' friends by default: photos, posts, friends list, but not private messages.

None of that data is actually particularly scary by itself, although I wouldn't enjoy the thought of it all being out there.

What Cambridge Analytica was bragging about was their big data model promising to distill users' data to a psychographic profile.

There's this story about 30 "likes" (of books / artists/ movies/ etc) being enough to predict peoples' sexual orientation with higher accuracy than the coworkers sharing a desk with someone.

The large publicity for such "big data" methods in the last years may have contributed to the change in public opinion, and (part of) the reason Facebook is just now getting its 15 minutes of infamy.