For normal sublist views you should be able to just customize the view and create two different versions with different names and restrict the different views to the relevant roles.  This specific case looks like it’s related to the project module so you may have some special challenges around the project tasks sublist view that are not applicable to sublist views in general.  Unfortunately, I don’t have the project module in my current account, so I can’t validate, but creating two different views with the column added and removed would be my preferred way to do it if it is possible.  Give it a shot and see if it works.