These caps are installed by the Plumber for the plumbing inspection. In this case the caps are still on years after the inspection and should be removed.

Example of how it effects the plumbing:
If you had a gallon jug full of water turned it upside down the water will struggle to go out due to the lack of airflow. It might gurgle because of not having sufficient air flow and in this case might cause it to smell or gurgle at the drains.