The biggest hurdle for Linux users is the FRC Driver Station. Sure, you can definitely program on any OS, but to control the robot itself... I faintly recall someone working on a portable, Python version of the driver station (barebones).
As for IDE, I'm still a GUI fan (I have an interesting aversion to vim). Nevertheless, I like my IDEs light - I use Geany for the majority of my code editing. (For Windows users, this is an amazing counterpart to Notepad++!)
I'm not sure how C/C++ can be compiled on Linux, simply because what you compile might not be compatible with the cRIO. When you compile something, you are usually compiling it for the current system. Most compilers compile for x86, which I'm 99% sure
isn't the cRIO's processor!
If you want to, you can find the cRIO's processor target, and then build the GCC cross compiler for that particular processor target. (I have a few BASH scripts to do that - if you're interested in attempting this, free free to ask) Even then, you will also need the FRC specific headers to make things work.
It's hard, but it's possible!
EDIT: Based on the screenshot found
here (my team programs in Java, not C/C++), it looks like the processor is a
MPC5200 processor or similar. (This one is based on a PowerPC CPU core.) Happy hacking!
