That is odd. Not sure why that would be. I have seen similarly strange (and likely unrelated) things as well. For example, I have 2 displays. When I stream through Spotify my left monitor goes blank until I stop streaming. Amazon Music doesn't do this. A co-worker has the opposite experience. When he streams Amazon, his right monitor goes out. Spotify doesn't affect his monitor. It really is the strangest thing.
I assume you are using a browser to stream music. What music service and what browser are you using?