Where did you find anything like Hide Thunderbird? Are you sure you did not have an add on installed that did this? I have used it for quite a while and have never seen anything like that.

Thunderbird sure has no control over operating system shortcuts.

Every Application is supposed to support and include a set of system calls and a standard set of menu commands. that is a big part of what makes Macs easy, they all work the same way. SAVE, PRINT, QUIT, COPY, PASTE, HIDE, NEW AND OPEN are all standard commands that belong in the 1st 2 menus with the corresponding commands Of Command "S","P", "Q", "C", "V", "H", "N" AND "O". Some few applications change these for special purposes, but 90% of applications use them just as they are. Thunderbird used to because I always use command "H" to hide it when I'm not doing email, same with Firefox, it is just in the background. I have attached the Firefox Menu (which is correct) and the new Thunderbird Menu which is not.

Are you using a non default theme?

I have never touched anything about the themes. I am using it as default as possible.