If anyone still interested, new version of this small add-on!
Major change
From this version I decided to store favorite modifiers in User Preferences since it should not depend on scene and be everywhere the same. So, from now to save changes go to Preferences → Save Preferences .
How to install
Go to Preferences → Add-ons → Install… and select “Blender_2.8_Favorite_Modifiers_Add-on_v1.1.0.zip”.
Enable add-on.
But be aware that FBX Game Engine Export Add-on is not really finished and not actually published for community.
I use it for my internal purposes and don’t have plans right now for publishing it.
However feel free to PM me for any questions!