In ZBrush 2020.1.4 (Windows 10, program started as Admin) deactivating One Open Subpalette doesn’t seem to work for me (shift clicking sub palettes works, though). Deactived Auto Collapse as well.
Works fine for me. 
By deactivating “One Open Subpallette”, I assume you want to keep more than one subpallette open at a time. This works for me, but there are other settings in the preferences that may modify or conflict with this.
Make sure both the left and right tray auto collapse buttons are off if you’d like this behavior in both trays. Also explore the sections “UI Groups” and “Subpallette Popups”. Read the descriptions by holding down CTRL when you mouseover, and disable anything you think might be causing a problem.
Also remember, you must store the config (Config> Store Config), to have any changes you make in the preferences persist when you restart the program.
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Thanks a lot for the extensive answer, Spyndel!
I confused UI groups with sub-palettes, so it was AutoClose UI Groups that I needed to deactivate.