Comparing Elixir and Go is reasonable, but I don't think Elixir and Rust have much overlap in the types of projects you would choose them for.
In fact the opposite is true! Rust is a pretty popular choice for writing native code (NIFs) for Elixir. (Similar to Ruby FFI).
See https://github.com/rusterlium/rustler
Discord especially has several real world use cases where they've implemented native code in Rust.