Rust normally prevents a lot of memory safety problems, but those are not the only kind of security problem in a crypto system. Obviously the library has to correctly implement the spec (and expectations of users), which just using Rust doesn't guarantee. More importantly, a crypto library also has to avoid leaking crypto data through various side channels. Just using Rust doesn't help with that; "Crypto Coding" at https://github.com/veorq/cryptocoding lists some rules to help address that.
Anyone know if rustls has worked on those issues as well? I notice that rustls uses ring, which asserts on https://github.com/briansmith/ring that "Most of the C and assembly language code in ring comes from BoringSSL, and BoringSSL is derived from OpenSSL. ring merges changes from BoringSSL regularly."
It doesn't matter if it's fast if it doesn't do things correctly...!