The log file indicates that the Preferences database is corrupt, which would explain why the things you are attempting to change are not being saved, as these changes are saved in the Photo Mechanic Preferences database.
From the article linked below, follow steps 1-5:
https://docs.camerabits.com/a/solutions/articles/48000341456Then, quit Photo Mechanic and open Finder
Choose the 'Go' menu from the top of your screen and hold down the Option key on your keyboard
With the 'Option' key held down, 'Library' will appear. Click on that and a Finder window will open to the 'Library' Folder
In the Library folder, locate Preferences and open it.
In Preferences, locate 'com.camerabits.PhotoMechanic' and rename it to 'com.camerabits.PhotoMechanic-OLD'. Finder may ask if you are sure that you want to change the name of this folder, so you should allow that, if prompted.
Launch Photo Mechanic again, and follow steps 7-10 from the article linked above (ignore the part about the 'other computer' in step 7, just do the whole thing on the computer with the problem)