Should I be taking iodide away from food?

You can take iodine whenever you want. Sometimes with food, sometimes without food. It doesn't really matter. It's more important to keep the selenium away from food. 

The reason I say this is because iodized salt has been added to foods for many years. And it has clearly been effective at treating iodine deficiency. So I see no reason to take the iodide away from food.

If you want to be safe though, you can just take it away from food. And just take it at the same time as selenium.