I would leave the ‘USB Debugging’ ON (enabled), just in case
As long as you have only allowed your own computer a trusted connection, the computer and the smartphone at the same time do not fall into foreign hands and your Fairphone has a lock pattern or password, there are, in my view, no relevant security concerns that make it worse than before.
Google notifications now keep telling me that my data are not saved. My pics & videos are now stored on a local HD so it’s Ok, but I’m still concerned about my OTHER data (contacts, apps data, …). Can I simply resume backups on my Google account (without triggering the whole ‘reboot’ dilemma again)?
That’s strange. I observed the same behaviour on my smartphone when I deactivated the GMS, but not when I reactivated it and deactivated the Google Play Store. The Google Play Store is also not actually responsible for backups.
Has anyone heard of other phone brands having experienced the same issue, or is this a FP specific problem?
Not yet. It seems to be a problem of the Fairphone-specific Android operating system in connection with the Google Mobile Service. This also happens with other manufacturers, but it’s a bit annoying because Fairphone updates have led to other problems more often lately.
Who could (be ready to) fix an issue that only affects such a small community?
The community is bigger than you think 
For the step forward (and discussion): any news on an official fix?
I don’t think so. someone else feel free to improve me. It will also be a bit difficult to rollout a fix Update when every “infected” smartphone is continuously rebooting… In addition it’s not easy to find such a problem… We need to help ourselves at first and then hope for a good plan.