I think I have had this problem a long time ago and I can’t remember what the solution was.
When I play Wow classic at random times my character panel random appears. I have checked the obvious if the ‘C’ key was stuck and it isn’t (and it doesn’t appear in other applications).
I have noticed that it especially appears if I shift click a player in chat to get info on him. It is not an inspect window that appears but my own character panel.
I play on Mac by the way. I also have a PC and the problem is never there.
Hello Eselar 
The behaviour you described it’s something I have seen happening with certain interface modifications and keybindings setup.
Would you be so kind as to try resetting your UI and also resetting your keybindings completely?
Hello,
Same problem here for me, on Mac too. Tried what Felranys said but it doesn’t work. The only solution I have is to debind the character panel keybind.
Help please
I had the same problem and it drove me crazy for months.
I’ve just realised I’ve got a keyboard shortcut for dialling out on a soft phone and this same shortcut was causing the character screen to open despite the softphone being closed. In this case it was Ctrl + D. I would check for any other application that has keyboard shortcuts and either change or remove them.