Apple's "services" apps–App Store, Music, Podcasts, TV–are the worst apps on the platform, period. They're so awful that I cannot understand how a sane developer could ship something like that.
To enable/disable shuffle after selecting a song, you must tap a bar near the bottom (which gives no visual indication that it expands); once expanded, you must then tap an unlabelled button with a “list” icon. This will show your upcoming queue, but also holds the control for shuffle and repeat. These are also unlabelled, but at least the icons are fairly unmistakable.
