What a journey … starting with pip install wxPython leads to errors over errors, missing prerequisites, errors while running alternate pip- and apt-commands you can find with google to solve the problems with wxPython.
For example:
sudo pip install wxpython leaded to starting an installation but then breaking on ModuleNotFoundError: No module named ‘attrdict’. Then pip install attrdict installed it successfully, still sudo pip install wxpython again complained about attrdict missing.
After getting out of ideas and pages google offered me with (partly or non-)working solutions, I retried pip install wxPython and this time it not only started downloading, it also started a build process and installed successfully in the end. It seems on my journey I collected all prerequisites and updates needed on my linux.
I guess it would be of help to have a list of all needed prerequisites and then offer a script with sudo apt-commands that will install all of them before running pip install wxPython
Many thanks to all of you who answered 