It is very common for me to be watching or listening to a stream... and then when they turn on some music that I don't like, I turn off the stream.
Please set it up so that I can choose whether to listen to the music that the streamer is broadcasting.
I'm 99% sure this is impossible for Twitch to do, given the way streaming works.
A broadcaster is using an application to send the audio/video to Twitch - the audio layers are mixed on the streamer's computer/software, and compressed down to one layer when they are sent over. It would require music-free streaming + Twitch adding music (and thus the option to then disable it), which is not how most streamers work.
I think at one point there was talk about a way to do something *like* that for the sake of copyright/DMCA removal? But I think that required the streamer to still do something different from what they're doing. So while it could be an *optional* feature in theory, I doubt it will ever become a Regular Thing that you can do on all or even most streams.