Firstly, we have a vocabulary problem which your images make clear.
What you call the VASL preferences (those under the General tab), I call the VASSAL preferences because they are created by and managed by the VASSAL code and are independent of the VASL module.
What you call the VASSAL preferences (those available from the File menu on the VASSAL window before opening the VASL module), I don't call anything because I have never used that way to access them in my life. I load the VASL module and then open preferences so I have access to the full range of preferences.
What I call the VASL preferences (those under the VASL tab of Preferences once the VASL module is started), apply only to the VASL module. I point them out to you in case you haven't been using them, but they have no impact on the Wizard issue.
All that just so we are talking about the same things.
At present, I cannot replicate the problem you are having. I work on Windows and sometimes VASSAL/VASL behave differently for MAC users. So there's that.
When I clear the checkbox on the Wizard screen and then click the Cancel button, it does change the preference in the General tab of the preferences. And the next time I start VASL I don't get the Wizard. That is the behaviour that you want. I don't know why it is not working for you. Maybe some other MAC users can test this on their system and see if they get the same results as you do?