Redox installation incompatible with "normal" Rust?

When trying to do a “Manual Setup” of Redox - as mentioned on -
I figure out that my Rust installation, which I use on a daily basis, becomes a problem:

$ curl -sSf | sh
info: downloading installer
warning: it looks like you have an existing installation of Rust
warning: rustup cannot be installed alongside Rust. Please uninstall first
warning: run /usr/local/lib/rustlib/ as root to uninstall Rust
error: cannot install while Rust is installed

Why is it not possible to have 2 rust installations ? What is in the way ?

I ran into this issue on solus as well. Rustup will let you have multiple version of rust installed, but only if managed by that tool. The conflict comes by when you run rustc or cargo which do you run? The rust up version or the system version. How I fixed it was by uninstalling rust from the solus repo and installing the stable and nightly version of rust through rustup.

You must use rustup and only rustup to have multiple Rust installs