As you probably know by now & as I understand it, this is a security measure, which will trigger Marshmallow to pop-up 'Screen overlay detected...' warnings each time you try to change an app's permissions (i.e. for the apps that are affected by this 'drawing over other apps' feature).
There are 2 ways to get around this so you are allowed to freely change apps' permissions (do one or the other - whichever is more convenient for you):
1. Go to Settings > Apps > access 'Advanced' (near the bottom) > under 'Advanced' subsection, access 'Draw over other apps'. Here, individually change the settings of
ALL the apps to 'No' (in other words,
disable 'Permit drawing over other apps' for
every app). Once done, you can freely change apps' permissions in Settings > Apps > [name of app] > 'Permissions'
without the annoying 'Screen overlay detected...' warning popping-up every time. Once you have correctly changed the permissions (for every app that's not working properly), you should return to individually change each of the apps' settings to 'Yes' in the 'Draw over other apps' section (in other words, re-enable 'Permit drawing over other apps' for every app).
or (easier for me)
2. Reboot your phone into Safe Mode (
click here if you need to know how). Once in Safe Mode, you can freely change apps' permissions in Settings > Apps > [name of app] > Permissions
without the annoying 'Screen overlay detected...' warning popping-up every time. Once you have correctly changed the permissions (for every app that's not working properly), restart the phone as normal.
For
both of the above & If you prefer, all changeable apps' permissions can also be easily done via Settings > Apps > access 'Advanced' (near the bottom) > access 'App permissions'.
If some apps are still not working as they should, check to see that the affected apps have 'Yes' below their name in the Apps > Advanced > 'Draw over other apps' section, AND they have ALL their permissions enabled under the Settings > Apps > [name of app] > 'Permissions' section.