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No, the presumption is that order matters in projects, and so OmniFocus will only reorder actions in a project upon command. If you make a context mode perspective using a focused project (select the project(s) in the sidebar, focus, switch to context mode) you can group by project and sort by due date, which should give an approximation of what you are trying to do, and that display will update automatically. Note however that because you are only changing the display ordering with the view bar, not the actual order of the actions, the order you see in that display will not necessarily be the order in which you would see the actions presented to you if you viewed that project in a next action view.