I definitely have this problem. Galaxy S5 will not download the feed pictures from my home wifi on the Facebook app. Works fine everywhere else, works fine on 4g, but no good on my S5. I can use a browser to go to facebook and it works fine, just not the app. Even got a new replacement from the factory for a different problem and expected it to be fixed. Opened it up and didn't even put the Sim card in. I loaded the facebook app and it worked well. Success! Loaded more apps and the sim chip and no luck with the facebook app. I have another Samsung product, the Note 2 and it works fine on it.
I did some research and it seems to boil down to IPv6 settings. Apparently the new facebook app is compatible with those. Everyone said to try turning the IPv6 off in the router, mine was already off. I just turned it on, deleted my facebook app, restarted my phone, loaded the facebook app., and for now at least it is loading the feed and it's photos at a normal looking rate.
Keeping my fingers crossed!