Could be an issue, but it's one with various possible solutions. Devs could switch to the LLVM-backed compiler periodically, a continuous integration system could run both compilers, etc.
If both compilers are relatively bug-free it shouldn't be too much of a burden. Correct C/C++ code runs fine under both GCC and Clang, for example. If anything, things should be easier with Rust, as it gives you less opportunity to shoot yourself in the foot in strange compiler-specific ways than do C and C++. I recall having a C++ alignment issue that only arose in one compiler, for example. (Of course, my code was broken, but it worked ok with one of the compilers just 'by coincidence'.) I figure that kind of thing is less likely in Rust, but I don't know the Rust language well enough to say this with confidence.