I wish all apps respected the SYNC button. If I turn sync off, apps that are properly coded will effectively stop notifying me and using background data unless I open the app and manually request an update, but most apps don't 'listen' to the SYNC button state.
And since on my tablet for some reason these apps don't have the option to disable background data, it looks like I'm screwed.
Instagram will take notification toggles universally, so if I disable it in the tablet, they're also disabled in my phone. Facebook is the only one I can turn notifications off for completely, but Messenger doesn't have a permanent 'off' switch for notifications (just up to 24 hours mute), and what's worse, even if you block notifications for Messenger in Android, if you use chat heads you STILL get those as a notification since they pop up over anything.