I am completing another setup using Ubuntu server + MATE 19.10 on a Raspberry Pi 4. This one will support more than one user.
Rather than placing the same two collections of customized backgrounds in each ~/Pictures/backgrounds directory, I made them global by putting them in their own /usr/share/backgrounds directories (eg. /usr/share/backgrounds/bg1 and /usr/share/backgrounds/bg2.
I also ensured that the ownership and permissions for everything match what was already there. To whit, 755 and root:root for directories:
drwxr-xr-x 2 root root 4096 Apr 29 15:48 bg1
drwxr-xr-x 2 root root 4096 Apr 29 15:48 bg2
and 644 and root:root for the files in those directories (such as these examples; there are 29 images between the two directories):
-rw-r--r-- 1 root root 7811 Jan 10 13:01 public.xml
-rw-r--r-- 1 root root 48162 Nov 17 2014 raspberry-pi.png
That said: When I go into the Appearances applet, I can add and apply them regardless of which username is logged in. However, if I exit the applet entirely and return to it later (say to change backgrounds), those items are no longer present and need to be added again! The only way an added item (image or slideshow XML) persists is if it's the active one.
As the subject line suggests, I don't know if the behavior in question is a bug or not. If anyone has a solution however, I'd be most appreciative.