What is the ruling on sitting with someone who is listening to haram (unlawful) things through headphones in the same room, without hearing what they are listening to?

You are not permitted to spy on others. If you are certain that someone is listening to something forbidden (munkar), you must enjoin them [to stop it], unless you fear a greater harm. If they do not stop, there is no sin upon you in sitting with them if you have a need to, as long as you do not see or hear the forbidden act. If they are listening to musical instruments (ma'azif), and you enjoined them but they did not stop, you are not obligated to leave the gathering even if you hear the music; because what is forbidden is listening intentionally, not merely hearing unintentionally.