Facebook and privacy have never been good friends, it doesn't matter if you use it on your mobile or the desktop version. The thing is, whatever they're collecting HAS ALWAYS BEEN THERE IN BLACK AND WHITE. We just don't care to read the fine print and raise our hands to the air and panic because someone yelled that the sky is falling.
Yes, it's safe to have the app on your mobile if you're a fan of Facebook. No, it's not safe if you don't want every bit of your life out there...but if you did, you wouldn't have joined Facebook in the first place, now would you?