Are you sure that MakeHuman was given permission under the System Preferences, Security & Privacy, General tab?
Some people have not been able to run the program because of this requirement.
It is possible to install the latest MakeHuman 1.2.0 release from the source code.
This is known to work up to Catalina (10.15.7)
If you follow the source install instructions at
https://github.com/makehumancommunity/makehuman and the program still does not start, please post some additional information about the failure.
One issue not addressed in the installation instructions: If you have a problem using the old PyQt5 library version, then installing in a virtual environment is suggested.
There are some issues with creating an macOS installer package, including Apple's notarization requirements.