You do give up privacy just by having a profile on facebook. It makes it easy to tie your browsing habits to your account, even if you are logged out. See previous discussion : https://news.ycombinator.com/item?id=14694451
This is why I only check Facebook using Chrome, on my home computer, using Firefox for everything else (with ads/trackers etc blocked, obviously). And of course I've never installed any facebook apps on my phone. I have checked mbasic.facebook.com from my phone a couple times, in an incognito window; that seemed like it was probably a reasonable level of risk.