This is just a mini list of "regressions" to track GTK2 behaviours that are still missing/broken in GTK3.
Most notably, these are differences since the last GTK2 release of Ubuntu MATE - which was 16.04.
Themes: Cannot change colour
Unfortunately, GTK3's theming engine had completely changed and no longer works with this option.
You can still modify any theme by changing its colour values in a text editor.
Upstream bug report requesting functionality:
For Ambiant-MATE family and Yaru-MATE (>= 21.04) themes, a new project allows for recolouring:
Treeviews: No alternate rows colours
GTK2

GTK3

Upstream bug report:
Middle click dragging in Caja
A content menu is supposed to appear, but it currently performs the primary action (left click)
Scrolling over tabs
It use to be possible to scroll over tabs to change them. The feature was removed from GtkNotebook in GTK3, and as a result, every program will need to implement the same feature again.
MATE Issues (mostly fixed)
- https://github.com/mate-desktop/mate-terminal/issues/133
- https://github.com/mate-desktop/pluma/issues/271
- https://github.com/mate-desktop/caja/issues/896
- https://github.com/mate-desktop/mate-control-center/issues/445
- https://github.com/mate-desktop/mate-power-manager/issues/282
- https://github.com/mate-desktop/mate-applets/issues/398
- https://github.com/mate-desktop/mate-panel/issues/967
- https://github.com/mate-desktop/mate-media/issues/130
- https://github.com/mate-desktop/mate-system-monitor/issues/166
Upstream bug report:
Overlay/momentium scroll bar behaviour
Not a regression as such, but the default behaviour is debatable. This one will be a regression in GTK4. 


(or maybe it was just three years so it's already EOL).
Nevertheless, 
I had an idea I'll try... take 18.04 and build MATE 1.12 under GTK2... and see if that's technically possible or feasible.