No, you don't have to seal both sides if you don't want to. All you have to do it seal it so it closes the gap to airflow, and one side will do that. I personally prefer to seal both sides. Also, if you use tape to seal the gap you might want to consider sealing both sides because if you seal only one side you will have the sticky side of the tape exposed in the gap which will let it collect dirt and debris.

Hope this helps

Ken