Ha - problem solved! Kemper support had the solution - thanx to Burkhard!
A simple case of the pedal settings: morph > wah was activated. I wasn't aware that this setting also affected morphing via the morph button or via the slot buttons, but apparently this is the case: once I morph via the morph button or a rig button, the Kemper acts as if I had moved a morph pedal.
So as long as the setting morph > wah is on in the Pedals (or Pedal Links) menu, the Stage will react to morphing as if I had touched the wah pedal and temporarily activate the wah.
That's a funky one - nice to learn about the sophisticated pedal linking options this way!
I was having the same "issue" and it was driving me nuts. Thank you for sharing.