To reproduce the problem, I deleted ~/.rustup, then installed the stable version. But then:
$ rustup toolchain install nightly
info: syncing channel updates for 'nightly-x86_64-unknown-linux-gnu'
info: latest update on 2018-12-25, rust version 1.33.0-nightly (f960f377f 2018-12-24)
info: downloading component 'rustc'
82.5 MiB / 82.5 MiB (100 %) 60.4 MiB/s ETA: 0 s
info: downloading component 'rust-std'
71.5 MiB / 71.5 MiB (100 %) 60.9 MiB/s ETA: 0 s
info: downloading component 'cargo'
info: downloading component 'rust-docs'
info: installing component 'rustc'
info: installing component 'rust-std'
info: rolling back changes
error: failed to install component: 'rust-std-x86_64-unknown-linux-gnu', detected conflict: '"lib/rustlib/x86_64-unknown-linux-gnu/lib/libLLVM-8svn.so"'