How to automatically scroll ScrollViewer – only if the user did not change scroll position

You can use ScrollChangedEventArgs.ExtentHeightChange to know if a ScrollChanged is due to a change in the content or to a user action…
When the content is unchanged, the ScrollBar position sets or unsets the auto-scroll mode.
When the content has changed you can apply auto-scrolling.

Code behind:

    private Boolean AutoScroll = true;

    private void ScrollViewer_ScrollChanged(Object sender, ScrollChangedEventArgs e)
    {
        // User scroll event : set or unset auto-scroll mode
        if (e.ExtentHeightChange == 0)
        {   // Content unchanged : user scroll event
            if (ScrollViewer.VerticalOffset == ScrollViewer.ScrollableHeight)
            {   // Scroll bar is in bottom
                // Set auto-scroll mode
                AutoScroll = true;
            }
            else
            {   // Scroll bar isn't in bottom
                // Unset auto-scroll mode
                AutoScroll = false;
            }
        }

        // Content scroll event : auto-scroll eventually
        if (AutoScroll && e.ExtentHeightChange != 0)
        {   // Content changed and auto-scroll mode set
            // Autoscroll
            ScrollViewer.ScrollToVerticalOffset(ScrollViewer.ExtentHeight);
        }
    }