I have the same problem (iPhone 7p, Spotify premium), it seems like it is actually a problem on Snapchat's behalf. To temporarily fix it, I've turned off the notification sound in settings. For IOS, go to settings - notifications - Snapchat - sounds - select/swipe them off. You'll still receive your notifications, you just won't hear the sound. This will prevent music from stopping with every snap, but it may not prevent it from stopping while opening the app or a message/story.
