Having a start date on the same day or before due date remove it from "View by : due-date, ANY"
Note: I never used start date (don't know what's it's for), But 1/3 of the time I mistakenly enter my due date it in the start date instead. So above bug will happen often to me.
If configured, tasks with a start date will not be shown until the start date arrives. If you have Toodledo setup this way, you should see a message like this at the bottom of any list where tasks have been hidden: "3 active tasks are hidden due to your filter settings. Turn off filters."
If you click on the link "turn off filters", these tasks will appear. And there is a link on the filters toolbar at the top that enables you to toggle display of these tasks (Show/Hide Future Tasks).
Lastly, if you never use the start date field then you can turn it off in the "Customize fields" screen. This will prevent you from accidentally setting a start date.