This is a known and repeatedly reported issue which was sadly overlooked during the Catalina Betas by the Apple team. The issue is dubbed "white screen of death"
The problem mostly affects the 2018 Mac Mini running Catalina connected to a AMD Radeon RX570 or RX580 based eGPU.
The symptom is mostly a blank white screen (sometimes black or magenta) upon boot and excessive GPU heat which causes the GPU fans to spin to full speed after a while.
You have to do the following to live with the issue:
- When the white screen appears, turn off your eGPU for 5 seconds and then turn back on. The login screen should appear normally.
- Turn off "Start up automatically after a power failure" under Settings/Energy Saver
- Turn off "Install macOS updates" under Settings/Software Update/Advanced...
The last two actions are needed to prevent your Mac to boot to a white screen unattended causing your eGPU to overheat for extended periods of time (this might cause further hardware related problems).
See these discussions for more information:
https://egpu.io/forums/mac-setup/state-of-egpu-for-macs-catalina-10-15-update
https://egpu.io/forums/mac-setup/macos-catalina-tidbits-egpu-updates/paged/2/
https://forums.macrumors.com/threads/catalina-egpu.2193797/page-4?post=27853347#post-27853347
https://forums.macrumors.com/threads/mac-mini-2018-hot-egpu-fan-full-throttle-after-upgrading.2204860/
https://www.reddit.com/r/eGPU/comments/dex36o/egfx_breakaway_box_550_amd_580_catalina_troubles/