Sierra screensharing not working

Read & write permissions must not be changed , I thought in another way try to remove all contents of cookies , saved application state , safari ( except book marks ) , caches - no one agrees about removing specially caches from user library ( ~/Library ) to trash , restarting the machine & emptying the trash , as cookies , caches are temporarily files , once the are deleted , emptied from trash , new files are created once again .in special case > from system library > caches are removed ( otherwise it is avoided ) .

For home user account the permissions for read and write .

For shared folder :

For public :

For drop box :

I stated about user library /hidden library that is click on go to go folder type ~/Library and System Library : /Library

Did you ever tried to delete contents of them ? try it , there is no harm in it .

Also did you check the two boxes as in screen shot while doing screen sharing .

One more option in security and privacy > general > log out after 5 minutes should be unchecked as if it is checked the system will log out if you have set the timings .

It is a good news , that screen sharing is working 🙂 between two MBP .