Black screen after installing rEFInd in Ubuntu on Mac Mini

Try an SMC reset and a PRAM reset (hold the PRAM reset for at least three chimes so it activates several times).

If you cannot access the Apple boot picker menu by Option Booting, then your Logic Board has been bricked.

Hello,

By using rEFInd you may have critically damaged your Macintosh’s firmware. Generally using 3rd party EFI controllers on a Macintosh is not the best idea. You would have wanted to set your preferred startup system using System Preferences in macOS.

You will need to prepare a macOS installation disk using another Macintosh and fully erase your Mac’s hard disk. This should restore the proper firmware.

How to create a bootable installer for macOS - Apple Support

FYI, I've used rEFInd without any issues, although I've never installed it from Linux. On macOS rEFInd uses standard macOS utilities to configure the NVRAM Startup Disk settings. Installing rEFInd from within macOS will not harm the Mac.

Now on Linux I have had issues on the first gen 32bit Core Duo laptops where setting the NVRAM settings from Linux does seem to go haywire sometimes. Those first gen Intel Macs had some very quirky firmware. I do know that Ubuntu in particular has had a few cases where it could brick a Mac when configuring the Mac's NVRAM because of incorrect kernel configuration and Apple firmware bug (I don't recall the exact details, but it happened at least twice that I am aware of with their Ubuntu installers --- I call it an Apple bug too because making an NVRAM setting change for a boot setting should never brick a computer).