I currently build my nixOS packages with musl, clang, and uutils, and the difference from gcc/coreutils/glibc is unnoticeable. The uutils project is great
That's the inverse of my question. If Rust is going to replace things written in C, other stuff is going to want to dynamically link to it.
A statically compiled Rust based replacement for an entire distribution isn't a realistic proposition, unless you fancy downloading a gig or two every time there's a security update and everything has to be rebuilt.
Theoretically, you could dynamically link with other Rust code that exposes the standard C ABI. This used to be common for C++ code, when name mangling was different between different compilers and versions - so a C++ library that wanted to be portable had to expose a C ABI, and C++ apps would dynamically link to it by calling that C ABI. Of course, this meant no exceptions, no destructors, no std:: data structures, but such was the price.