This 'bug' has been annoying me too... I wondered if uninstalling and reinstalling might fix it. It didn't. But whilst reinstalling I noticed that there was Spotify for iOS4 available. And while installing that results in a 'black barred' experience with smaller screen estate, the app doesn't crash when the volume is changed. So i'm using that until Spotify/Apple manage make the latest app work with the latest OS.
Thank you for pointing that out, Gurkfil. I was about to upgrade to iOS 7 beta 4 from iOS 6.0.2, and I wanted to be sure the issue I previously encountered in beta 3 was fixed.
Long story short, I downgraded my iPhone 5 to iOS 6.0.2 just so that I could use Spotify and Skype again, but I think I could do without Skype (never really use it anymore), so I will go ahead and upgrade.