They probably have a fake JS app that uses the default media playback channel and not some kind of native app sound output. Muting then..
Music stops when I open the app
Switching off sounds both in the app itself (More > Settings > Board), and in iOS (Settings > Notifications > Chess) seems to work for me (except sometimes the first move…). I am intrigued that we can’t have both sounds from streaming apps and Chess together, and concerned that the dev seems to pay zero attention to feedbacks.
Turning off both Sounds and Haptic Feedback in Settings -> Board fixed the issue for me when playing music with iOS Music app

+1 this honestly makes me want to switch to another chess app. Especially considering it’s been almost 10 YEARS and no response from the company
It says you were on line a few minutes ago. So I guess it isn't such a big deal.

Chess.com get it together! For what you charge you need to provide a product that allows this basic feature!

Chess.com get it together! For what you charge you need to provide a product that allows this basic feature!
What do they charge to free members?

So for me it neither works in IOS to stop sound directly in the chess.com app settings nor in ios notification settings. You should really work on this and on your communication. There is no excuse

Switching off sounds both in the app itself (More > Settings > Board), and in iOS (Settings > Notifications > Chess) seems to work for me (except sometimes the first move…). I am intrigued that we can’t have both sounds from streaming apps and Chess together, and concerned that the dev seems to pay zero attention to feedbacks.
this worked for me but I did not turn any notifications off in IOS. I just turned off haptics, then killed music app, and then restarted the app and played music. Working now
Have audio off in settings and it still shuts down music audio anytime I use app - please fix this - thanks