is it possible you logged in using wayland instead of xorg?
just booted into mubuntu and didn’t see that as an option on the login screen.
Problem Overcome. Not really solved, since it seems to be a problem with the installation overall. But here goes.
I found the three libmarco files that the error logs say cannot be found, but in a different Maté installation on a different harddrive. I copied them to the directory:
/usr/lib
and tried Appearance again. Voilá.
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I would call that solved. 
Glad you finally got it sorted.
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agreed that it seems like a larger issue if some of your system files/utilities have gone missing. if it were my system, i would run fsck to make sure the file system basics were in order and then take a look at gsmartcontrol (a nice gui front-end to smartmontools) to make sure the disk itself is ok.
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The necessary lib comes with Mate 1.20
I have setup the PPA to get Mate 1.22:
ppa:jonathonf/mate-1.22
Then I get the same error: /usr/lib/x86_64-linux-gnu/libmarco-private.so.1 is missing, but /usr/lib/x86_64-linux-gnu/libmarco-private.so.2 is present.
So to fix this, I just linked the lib:
sudo ln -s /usr/lib/x86_64-linux-gnu/libmarco-private.so.2 /usr/lib/x86_64-linux-gnu/libmarco-private.so.1
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