Make no mistake: this is user-hostile. Facebook is actively creating channels to continue refreshing their app in the background when the user has explicitly stated that they do not want it to. Ironically, the best way to reduce the battery and data consumption of the Facebook app in the background is to switch Background App Refresh back on. Better still, remove the Facebook app from your phone, and perhaps replace it with Paper (US store only).
Every time I take a look at a friend's iPhone, Facebook is the app with the highest amount of battery usage in the background – even with Background App Refresh turned off. This has been going on for years, and instead of fixing the issue, it does seem like Facebook is always coming up with new ways to circumvent user control and consume more energy.
The fact that a company the size of Facebook can't optimize energy consumption of their iOS app is simply ridiculous. If they can but don't want to (because of processes they want to run in the background, constant notifications, etc.) – well, that's even worse.
My solution has been the same for the past couple of years: never install the Facebook app, and always access Facebook from Safari.
I’ve never been much of a fan of Facebook, and this sort of thing just adds fuel to that particular fire.