If you use official compiler builds (such as from rustup), they are disabled in the stable and beta channel, enabled on Nightly. If you build Rust yourself from sources (which includes building LLVM), they are disabled in the default configuration.
The Rust team recently added builders to their Travis-CI configuration to also make Nightly compilers with LLVM assertions disabled, for a few host platforms. These builds are published at https://s3.amazonaws.com/rust-lang-ci/rustc-builds-alt/SHA1/rust-nightly-HOST.tar.gz, where SHA1 is the hex hash of a merge commit into rust master, and HOST is a host “triple” like x86_64-unknown-linux-gnu.
However, rustup doesn’t know about these builds so you’d have to download them yourself. (You can use rustup toolchain link after that.)
If you build Servo, you have nothing to do as I’ve made these new compiler builds the default. (Except for some of the CI builders where we enable assertions back, in case they help catch a compiler bug.) Servo has had its own bootstraping mechanism (written in Python) for downloading a Rust compiler since before rustup existed.