Exactly like this: https://github.com/mate-desktop/mate-panel/issues/249
When compiz starts, mate-panel turns unclickable for some reason and the only way to fix it is to run mate-panel --replace
I have experienced this after next boot when trying out compiz with mate, but I did not run the command. The panel just fixed itself after a while. Perhaps by opening Firefox.
Appears to be an issue with compiz itself that was resolved since their last release. I welcome any patches for it.
This was most likely fixed with 0fb5a75b96b6