I have a similar problem with 5.7 and 6. I keep getting messages saying I haven't turned on Sync. I don't want to turn on Sync; I want to be able to turn it off permanently, and not get any more messages about it. Grrrr!!!
I HATE THIS TOO. IT IS STUPID AND ANNOYING!!!!
Go to space just above navigator where your name is located. click. in the drop menu select the pause symbol for LR mobile sync.
I believe this turns it off ONLY for the current catalog. For those of us who have thousands of catalogs, this still requires an ANNOYING sequence of steps every time you open a catalog.
Lightroom really needs to develop App-wide preferences and settings, instead of having to manually set preferences for each catalog.