To put it into perspective, I was unable to change the items in Devel Config Editor, either. And that's really strange. It supposedly saved the modified entry, I got a message to that effect, and nothing was actually changed in the database, reading the same entry again re-loaded the unmodified, original contents of the config entry.

Actually, after making a backup, I simply decided to delete all items where there was a language variant of any config object and it works now. But isn't this a bug in Drupal? I wouldn't expect adding and removing a language to cause such problems (at least, removing a language should remove all related config items). I never had anything similar in earlier Drupals, although the config system is very much different now, that's for sure.