Ever since I upgraded my Samsung Galaxy S Vibrant to the S4, I have been getting these notifications to 'Log in to sync Facebook with your other applications'. The weird thing is that I already had the Facebook app and have been using it. I dealt with it for awhile until recently. After searching online I found out how to disable it and wanted to share.
Open Settings > More > Application Manager
Swipe over until you are looking at 'All' applications
Scroll down and look for SNS - It will have a Facebook icon
Select SNS and then choose to Force stop and Turn off
What the annoying notifications look like for reference: