I get this message ("User Data Files Cannot be Synced for this Game") every time I play a game (Divinity, Original Sin 2). Why? Is there something I can do to prevent this? What are the ramifications? I usually hit "ignore"; is the the correct response or should I be using "sync to this machine"?

I recently started getting this message for Batman: Arkham Origins. Didn't happen for the first week or so of playing, now it asks me to choose which source has the most up-to-date save file: the cloud or my PC.

Is there a way to fix this so it goes back to auto-syncing without my intervention?

Well, I would suggest just uninstalling galaxy and backing up your saves manually, at your command, in your way, without reliance on third parties.
If you want to test which save you want, I would suggest, move all the saves from your hard drive to another folder, eg. C:/temp, then run the game via galaxy and let it download the most recent from then. You then have both sets of files and copy paste them in at will and decide what you want to keep. See how much power you can have without a client! Oh, do bear in mind you likely have to delete saves from within game or something for galaxy to realise.

+1

It's difficult to say, but most likely what happened is that when you last exited the game your Internet connection was down, so Galaxy wasn't able to upload your save to the cloud. And now when you start the game, Galaxy sees two different saves. In most cases, you should always choose to use the save on your system as the most up-to-date. Once you chose that, Galaxy shouldn't ask you anymore, at least until the next time this unlikely sequence of events repeats itself.

HYPOTHETICALLY: It might happen, that if your HDD/SSD is failing your save on your hdd could have become corrupt after Galaxy uploaded your save to the cloud, and therefore you should use the cloud save as the most up-to-date. This case is extremely unlikely, so you shouldn't even consider it.