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.
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.