You can't The process has to have permissions to act on the files it syncs. Not to mention, syncing system directories like /etc and /var is typically going to be a bad idea, as they often contain special file types (like socket files or symlinks) or database files. If you're going for a backup system, there are a bunch of better suited tools then a one-way Syncthing instance.
Edit: I should clarify, that you can read any file that the Syncthing user can read, likewise with writes. There are numerous files in /etc/ that are read-only for root, meaning those will not be synced, and none of the files would be able to be overwritten when syncing from another device.