"The child wears the shirt because it is clean."
Translation:Het kind draagt het hemd, omdat het schoon is.
In this cause because indicates a reason (there is human reasoning involved), the reason why the child wears the shirt is the shirt being clean. Doordat can only indicate a cause (with no human reasoning involved).
Omdat can both indicate a reason (like here) as well as a cause. In the following sentence it would be possible to use both omdat and doordat because there is a cause and no human reasoning is involved.
- Het hemd is vies, omdat/doordat het in de modder ligt. - The shirt is dirty, because it is lying in the mud.