Why does opening the camera app pause music or podcasts on an iPhone 6s?
Live photos use the microphone to record sound as well as video when you take a picture. Look at the camera settings when you open the app to see whether video is going to happen (or already be happening since it records video from before you press the shutter).

There appears to be a bug (that hasn't been fixed yet as of iOS 9.3) on that hardware that makes iPhone 6S worse than others - it pauses even when you are aware of the video aspects and request a non-live photo and non-video recording setting.