Views are fundamentally structured in a hierarchical fashion, so applying sorts outside of the hierarchy of the view doesn't really make sense. Even if your view is set up to look like an Excel range of cells, Tableau is still interpreting it as a hierarchical arrangement of dimensions. That's unlikely to change.
Changing the column to sort on is akin to changing the hierarchy. So one thing you can do is create separate views, each with a different sortable dimension positioned at the top-most level of your hierarchy. Then, create a parameter that the user can use to select which column they want sorted. Filter each sheet so that it only displays if the appropriate parameter value was selected. Finally, put all your sheets together on a dashboard, along with the parameter, so that when the user changes the parameter values, the sheets appear to "replace each other" on the dashboard.
See this article for more information:
Hope this helps!