Anyhow, here's the bug report itself:
The Steam release of FTL on Linux packages a bunch of library files in "~/.local/share/Steam/SteamApps/common/FTL Faster Than Light/data/<arch>/lib" and then dynamically links against them when running. This causes problems because the libstdc++.so.6 file provided with FTL is an older version than is required by my graphics drivers. In my case, this causes X to crash and bump me to my KDE login screen. That's very distruptive, because it can lose data held by other programs running in that X session at the time. It also prevents FTL from running at all.
I am running 64-bit Gentoo Linux.
Here's an unhealthy run of FTL:
chad@Hugin ~/.local/share/Steam/SteamApps/common/FTL Faster Than Light/data $ LIBGL_DEBUG=verbose ./FTL 2>&1 | tee ftl.log
Loading Arch = amd64
libGL: OpenDriver: trying /usr/lib64/dri/tls/r600_dri.so
libGL: OpenDriver: trying /usr/lib64/dri/r600_dri.so
libGL error: dlopen /usr/lib64/dri/r600_dri.so failed (/home/chad/.local/share/Steam/SteamApps/common/FTL Faster Than Light/data/amd64/lib/libstdc++.so.6: version `GLIBCXX_3.4.14' not found (required by /usr/lib64/dri/r600_dri.so))
libGL error: unable to load driver: r600_dri.so
libGL error: driver pointer missing
libGL error: failed to load driver: r600
libGL: OpenDriver: trying /usr/lib64/dri/tls/swrast_dri.so
libGL: OpenDriver: trying /usr/lib64/dri/swrast_dri.so
libGL error: dlopen /usr/lib64/dri/swrast_dri.so failed (/home/chad/.local/share/Steam/SteamApps/common/FTL Faster Than Light/data/amd64/lib/libstdc++.so.6: version `GLIBCXX_3.4.14' not found (required by /usr/lib64/dri/swrast_dri.so))
libGL error: unable to load driver: swrast_dri.so
libGL error: failed to load driver: swrast
No settings file found!
Initializing Crash Catcher...
Initializing Video
Video Initialized
GL_ARB_framebuffer_object not supported.
Opengl version = 1.4 (3.0 Mesa 9.1.2)
Starting audio library...
Audio Initialized!
Resource Loading Failure (or voluntary quit)!
... At this point I ctrl-C, otherwise it will eventually kill my desktop environment. ...
I am on a 64-bit machine, so I moved data/amd64/lib to data/amd64/lib.bak and then made a new data/amd64/lib directory that contains only symlinks. At that point I did a pick-and-choose depending on which libraries I felt should be loaded from the game and which should be loaded from my system.
Here's my fixed up data/<arch>/lib directory:
chad@Hugin ~/.local/share/Steam/SteamApps/common/FTL Faster Than Light/data $ ls amd64/lib -l
total 0
lrwxrwxrwx 1 chad chad 21 May 24 01:25 libIL.so.1 -> ../lib.bak/libIL.so.1
lrwxrwxrwx 1 chad chad 22 May 24 01:25 libILU.so.1 -> ../lib.bak/libILU.so.1
lrwxrwxrwx 1 chad chad 23 May 24 01:25 libILUT.so.1 -> ../lib.bak/libILUT.so.1
lrwxrwxrwx 1 chad chad 24 May 24 01:27 libSDL-1.2.so.0 -> /usr/lib/libSDL-1.2.so.0
lrwxrwxrwx 1 chad chad 21 May 24 01:25 libbass.so -> ../lib.bak/libbass.so
lrwxrwxrwx 1 chad chad 24 May 24 01:25 libbassmix.so -> ../lib.bak/libbassmix.so
lrwxrwxrwx 1 chad chad 25 May 24 01:26 libfreetype.so.6 -> /usr/lib/libfreetype.so.6
lrwxrwxrwx 1 chad chad 24 May 24 01:25 libpng12.so.0 -> ../lib.bak/libpng12.so.0
lrwxrwxrwx 1 chad chad 23 May 24 01:26 libstdc++.so.6 -> /usr/lib/libstdc++.so.6
lrwxrwxrwx 1 chad chad 16 May 24 01:29 libz.so.1 -> /lib64/libz.so.1
With my new library directory humming along nicely, I am able to run the game. (Honestly I haven't tried gameplay yet. I am about to go to bed and then go to work tomorrow, and playing FTL would probably be exclusive to both of those activities.

Here's a healthy run of FTL:
Loading Arch = amd64
libGL: OpenDriver: trying /usr/lib64/dri/tls/r600_dri.so
libGL: OpenDriver: trying /usr/lib64/dri/r600_dri.so
libGL: Can't open configuration file /home/chad/.drirc: No such file or directory.
libGL: Can't open configuration file /home/chad/.drirc: No such file or directory.
Initializing Crash Catcher...
Initializing Video
Video Initialized
Opengl version = 3.0 Mesa 9.1.2
Starting audio library...
Audio Initialized!
Resource Preload: 8786
Initializing animations...
Animations Initialized!
Loading Ship Blueprints....
Blueprints Loaded!
Initializing Sound Data....
Generating world...
Loading achievements...
Loading score file...
Running Game!
More useful data; here are the versions of GLIBCXX provided with FTL:
chad@Hugin ~/.local/share/Steam/SteamApps/common/FTL Faster Than Light/data $ strings amd64/lib.bak/libstdc++.so.6 | grep GLIBCXX
GLIBCXX_3.4
GLIBCXX_3.4.1
GLIBCXX_3.4.2
GLIBCXX_3.4.3
GLIBCXX_3.4.4
GLIBCXX_3.4.5
GLIBCXX_3.4.6
GLIBCXX_3.4.7
GLIBCXX_3.4.8
GLIBCXX_3.4.9
GLIBCXX_FORCE_NEW
and here are the versions of GLIBCXX available on my system:
chad@Hugin ~/.local/share/Steam/SteamApps/common/FTL Faster Than Light/data $ strings /usr/lib/libstdc++.so.6 | grep GLIBCXX
GLIBCXX_3.4
GLIBCXX_3.4.1
GLIBCXX_3.4.2
GLIBCXX_3.4.3
GLIBCXX_3.4.4
GLIBCXX_3.4.5
GLIBCXX_3.4.6
GLIBCXX_3.4.7
GLIBCXX_3.4.8
GLIBCXX_3.4.9
GLIBCXX_3.4.10
GLIBCXX_3.4.11
GLIBCXX_3.4.12
GLIBCXX_3.4.13
GLIBCXX_3.4.14
GLIBCXX_3.4.15
GLIBCXX_3.4.16
GLIBCXX_DEBUG_MESSAGE_LENGTH
Before I had this particularly fortuitous debugging session, I had given up on running FTL on Linux and was using Windows instead. That's very inconvenient though, and it won't work for players that lack a dual boot. Please help the players!