Can't Open Sonic Pi 3.1.0... Error

There are quite a lot of differences, which you can see if you go again to the link I gave for the new version and then click on link aa4a8bb on 9 May (top right corner of the listing). This displays the differences that the commit encompasses.
However it doesn’t seem to solve your problem.
Another suggestion you might consider, would be to disable input altogether (which may be appropriate for your Mac Minis).
To do this you want to find the line 340 in the newer version or 332 in the older version, both of which read
"-i", "num_inputs",
and change the one you are using to
"-i", "0",
(Both lines are in the def boot_server_osx definition)
This will then disable audio input to Sonic Pi, but will hopefully let it boot on the Mac Mini.
It would of course prevent the use of commands like live_audio