I just received my 2018 Mac mini and connected it to my 30" Apple Cinema Display, along with the USB connection for the keyboard and mouse. I had tried (as a check) using the display with my MacBook Pro (11,5 mid-2015 version) with the Apple DVI to HDMI and it worked, but I did not try connecting the USB cable for keyboard entry.
With the 2018 Mac mini, using the same Apple adaptor and connecting the USB cable for keyboard and mouse, all I see is the light that says that the Mac mini and the display are receiving power. The display is blank.
I bought the display in December 2005, so, I probably should not expect compatibility at this stage, as some of my software programs have also been orphaned with the most recent OS updates.
I have ordered new peripherals, including a monitor, as I am guessing that I finally have to move on, given my infrequent use of this monitor and computer compared to my laptops. That may change.