There are some monitors, in my case Dell U2413, that report having YCbCr support when plugged in over HDMI. My AMD Radeon RX 570 Series video card sees this YCbCr pixel format and then prefers that over the RGB pixel format. The result is that fonts, graphics and other visuals are pixelated and not smooth in Ubuntu.
This actually is not just a Linux problem. A similar problem exists on macOS with the same monitor hooked up over HDMI. In fact an article by John Ruble on the Atomic Object blog called Fixing the External Monitor Color Problem with My 2018 MacBook Pro attempts to fix the exact same thing.
All of the articles I could find exploring this topic advocate patching the EDID for the monitor. Unfortunately the macOS solution would not work here. Luckily I found a Reddit post that covered how to get it working.