We experienced the same problem, so I did a bit of Javascript debugging, hoping to find a quick workaround. To cut a long story short: I succeeded. I found a method that delegates the mouse down event to all Drag&Drop behaviors like ColumnResizing and ColumnMoving. Firefox receives a special treatment here:

_onMouseDown: function(e)
{
    if (e.button == 0)
    {
        this._mouseDown = true;
        /* disable default drag-drop of firefox */
        if (!$IG.DragDropManager._supportsElemFromPoint || $util.IsFireFox)
            $util.cancelEvent(e);
    }
}

So the event will be cancelled as soon at has been consumed by the first behavior assigned which happens to be the ColumnMoving behavior.

So I’m using a litte Javascript method

function onInitMoving()
{
    $util.IsFireFox = false;
}

It is called on the client side event fired as soon the ColumnMoving behavior is initialized:

<ig:ColumnMoving Enabled="true" DragStyle="Slide" ColumnMovingClientEvents-Initialize="onInitMoving" />

This works for us and I have not experienced any unwanted side effects so far. Maybe this helps you too, at least until the Infragistic team releases a fix.