Does Rust have the same level of support for dynamic linking as C? Genuine question, I don't know the answer. Good support for dynamic linking is crucial for apps that get shipped in Linux distributions.
The hairy part is finding the library on the system, and that's a mess that Rust merely inherited. The build scripts are there to run pkg-config, search system lib dirs, and compile a fallback if necessary (next everyone suggests to just have Cargo automatically figure it out, until they see how deep the rabbit hole goes for snowflake libraries like openssl and llvm).