I experience the same issue on an iPhone 6Plus and an iPad Air.
I listen to music by streaming from my iOS devices to a loudspeaker via bluetooth connector (Philips AEA2700). Up until now the volume could be controlled through the iOS devices hardware buttons. Since my update to iOS 10.3 i can only turn the volume off that way, or on. Everything else must be done by loudspeaker remote.
Volume control on my girlfriends iPhone 5 with an earlier version of iOS works just fine.
Does anybody else experience the same issue? And have you found a way to work around it?