The problem is that you have to think about it at all. If you compile on a machine with a new libc, and then try to run it on a machine with an old libc, it won't work. So you end up doing what most people do, even outside of Rust, which is take the oldest CentOS box you can stand and do builds on that.
The Autopackage project had a solution for this problem years ago called apbuild. It would search for the versions of glibc symbols and use the oldest possible ones, which resulted in portable binaries. With some quick googling I found the code here: https://github.com/DeaDBeeF-Player/deadbeef-plugin-builder/t... Probably doesn't work anymore though :/
It's a bit sad that this is still unsolved, probably due to the GNU people's hatred for closed-source distribution.