People that matter have caught up with my observation about Linux Ubuntu 18.04 having issues with font rendering in Atom. There are actually three parts of the discussion I ran across while digging for a solution: Chromium, Electron, and FreeType. It turns out the system wide "fix" requires downgrading libfreetype6. I believe, but am not certain, the issue has been addressed in Atom 1.2.6, but this does not deal with Discord and other apps. While you can scale the font up in Discord's settings to make the problem less pronounced, it is not an ideal solution.
I followed these steps to resolve the issue on a clean install of Ubuntu 18.04 LTS.
sudo add-apt-repository "deb http://us.archive.ubuntu.com/ubuntu/ artful-updates main"
sudo apt-get update
sudo apt-get install libfreetype6=2.8-0.2ubuntu2.1
sudo apt-mark hold libfreetype6
| Canonical Bug Report | Atom Bug Report on GitHub | FreeType | Chromium | Electron | Atom | Discord | Ubuntu |
Disclaimer: this might not work for you, I am wrong a lot, be careful with sudo.