Launch OpenEmu, open preferences, and select cores. Right-click OpenEMU, and select open to bring up the prompt that will let you run the application. OpenEMU is open source but it isn't signed, you'll see an error if you try an execute it. Step 2: Safelist MAME (Big Sur 11.x and above) If I had to guess, it's likely because there are a few missing assets (the control menu for MAME doesn't have a skeuomorphic graphic, for instance), and it doesn't filter out BIOS files. I'm unclear as to why after years, the MAME version is still experimental. Regular OpenEMU does not support the MAME core, so you need to get the experimental version from. It's designed to be the one-stop-shop for Mac emulation, and it does a fantastic job.
OpenEMU is a beautiful core-based emulator (akin to RetroArch) that supports many game consoles.