Just wanted to report that I installed MacOS Monterey yesterday and have had no problems so far running any of my Mathematica applications. Your mileage may vary of course, so be careful.
I am running a 2018 Mac Mini 3 GHz 6-Core Intel Core i5 with 32 GB 2667 MHz DDR4. No Apple silicon yet, but Christmas is just around the corner.
I also installed Mathematica on my M1 Pro MacBook Pro running Monterey and have had no problems so far. One thing I did notice, however, is that the benchmark result seems to be incorrect. It gave the result as 0.5 but the M1 MacBook Air scored around 3 here. A few calculations I have tried have been pretty speedy so I think the benchmark result is erroneous. I'm wondering if this is because there hasn't been an update for Monterey. It would be interesting to see what happens on an Intel machine running Monterey.
I got a 3.56 on my Intel-based mini running Monterey.