I just try to ask this question over here, nobody apparently is able to answer this question:
On Android (>4.4) the SD card is not writeable, except for the Android/data/[package-url]/ directory. The solution to this is to root your phone and to edit a config. The phone is an LG Stylus2 and has Andoid 6.0.1. The phone does not allow to format the SD card as internal storage (which would resolve the problem)
BUT: when I install e.g. a file manager like "Simple File Manager" which is a normal apk like all others and installed on a non-rooted phone, the SFM has read/write access to the entire SD card. I asked the author of that package why SFM has R/W access to the entire SD card and his answer was:
Well the app uses the casual Storage Access Framework, thats the way SD card files have to be handled by all apps.
Nobody seems to know the answer to this question. Someone over here maybe?
P.S.: e.g. the F-droid app "syncopoli" has WRITE_EXTERNAL_STORAGE set and has no RW permission to SD card, except for its own dir. Remote to local works btw contrary to what the site says.
P.S.2: rsync wrapper even does not even propose dirs outside Android/data/[package-url]/ directory.
P.S. 3: I'm not the only one