Because this fix relies on modifying the composite manager, and you can only have one composite manager at a time, it is hard to do unless you already use a system that does not have a composite manger. I suspect that it is possible to apply the LD_PRELOAD to any composite manager, but the composite manager is specific to every OS and desktop environment. I also suspect that you can force your OS to use compton and the fix, but again that is specific to OS/Desktop Environment.
If you have a composite manager, skip this next section, if you do not have a composite manager, follow these steps:
Run the following command in your terminal and you will be all set, note that you must rerun this command every time you login, so I suggest putting this in your .bash_profile or .zprofile (if using ZSH).
LD_PRELOAD=/usr/lib/mumble/libmumble.so compton -CGb --backend glx --paint-on-overlay
The flags -CG disable shadow effects
The flag -b runs it in the background as a daemon
The flag --backend glx runs it using OpenGL
The flag --paint-on-overlay paints on X Composite overlay window instead of on root window. You can add the flag --vsync with an argument to enable vsync.
Run mumble. Because of the nature of the fix, you can start mumble after TF2 and still have the overlay show up. The overlay will appear whenever you are connected to a mumble server.
If you are like the majority of people and have a composite manager bundled with your OS, this task becomes more involved because you cannot have 2 compositors running at once. Please note that this fix is rather ugly and requires some time to set up and also requires you to logout every time you wish to use the mumble overlay. The following steps are paraphrased and modified from this guide.
Install compton and openbox (you can optionally install obconf and obmenu, but they are not necessary)
Create the directory ~/.config/openbox if it does not exist
In that directory create a file called autostart
In that file, place the following (any line starting with a # is a comment and it will not be run)
# Starts compton and is necessary for the overlay to work, look at the above section on compton to decide what flags you want to use
LD_PRELOAD=/usr/lib/mumble/libmumble.so compton -CGb --backend glx --paint-on-overlay &
# Autostarts steam
# Autostarts mumble (comment out to stop mumble from automatically starting)
# You also can place any program in here that you wish to start
# Use a & at the end of the name so that your computer does no wait until
# that program is fully started before it start the next program.
When you wish to play a game, logout of you account, and then select openbox as your desktop environment. This requires a login manager than supports multiple desktop environments. Most do, but it may require you to look around to find out how to switch desktop environments. If you are using startx/.xinitrc, make sure that you use exec openbox-session rather than exec openbox because exec openbox does not automatically load the autostart file.
To return to your normal desktop, logout of your account and then select your normal desktop environment from you login manager.