I've installed the 11.1 beta (of 2020-11-17) on an Intel-64 virtual machine and installed and run the test suite for the recently released 3.9.1rc1 Universal2 binaries from python.org. The tests, including tkinter tests, run similarly to how they do on 11.0.1. Further, as far as I can tell, there is no place within Python itself where such a message ("macOS 11 or later required !") is emitted; I did not search the Tcl or Tk sources since you didn't say which version is in use. Be aware that 3.9.1rc1 is the first official Python release that supports macOS 11 Big Sur so it may be that the brew version you were using has preliminary patches for Big Sur support that differ from the final versions. Depending what you are trying to do, you might want to use the python.org 3.9.1rc1 or 3.9.1 final (when released) until there is a supported brew version. Or, as Ronald suggest, you may need to track down exactly what and how the brew recipes are building for Tcl, Tk, and Python.  Good luck!