In the meantime - and I know this is awful - $HOME/.multirust/toolchains/nightly/lib/rustlib/uninstall.sh --component rust-std-x86_64-unknown-linux-musl might work.
It doesn't:
❯ $HOME/.multirust/toolchains/nightly/lib/rustlib/uninstall.sh --component rust-std-x86_64-unknown-linux-musl
install: error: Option '--component' is not recognized
I had to run uninstall.sh without --component, and hit this bug by doing so.