MacBook Pro Function key + Command/Option hotkeys problem
Sharing a solution to this problem, although it's pretty uncommon case.
Root cause of the problem was Karabiner elements setup.
They have a ticket open corresponding to this case:
https://github.com/tekezo/Karabiner-Elements/issues/1160

What you need to do to start registering this hotkeys is essentially enable unknown devices in Karabiner settings.