How do I use rules scheduler to disable and enable a commerce product entity based on certain date fields?
First create a Rules component for setting the status of a product.


Go to Configuration -> Workflow -> Rules -> Components -> Add new component.
Create an Action set.
Give the component a suitable name, such as Set product status.
Create a parameter of type Commerce Product, label Product, machine name product; and another of type Truth value, label Status, machine name status.
Add action: Set a data value
For Data, use the Data selector to select the product parameter's status (product:status).
For Value, use the Data selector to to select the status parameter (status).
Save


You now have a component that can be scheduled. Next you need to trigger the creation of the scheduled action. I'm going to describe the process for enabling the product; you should be able to create another rule for disabling easily enough following the same method.


Go to Configuration -> Workflow -> Rules -> Add new rule
Choose the triggers After saving a new commerce product and After updating an existing commerce product.
Add the condition Entity has field.
For Entity, use the Data selector to choose commerce-product as the entity.
For Field, use the dropdown to select your start date field.
Add condition Data value is empty.
For Data to check, use the Data selector to choose the start date field.
Check the Negate checkbox (we only want to proceed if the field is not empty)
Add another condition Data comparison and select the start date field is greater than site:current-date
Add an action Schedule component evaluation.
For Component, choose the component you created earlier.
For Scheduled evaluation date, use the Data selector to get the start date.
For Identifier, choose something like Enable product [commerce-product:product-id]
For Status check the box.
For Product use the Data selector to choose commerce-product.


Then in order to remove a scheduled action if the date's removed from the field:


Follow steps 1-7 (but not 8!) immediately above to create a new rule.
Add an action Delete scheduled tasks.
For Component, choose the component you created earlier.
For Identifer, use the same string you used before.


And another rule to delete the scheduled action when the product's deleted would be good too.

I quickly gave that a go and it seems to work for me. Let me know if you have any problems.