Imagine I have a galvanic cell where in one half cell there is a lump of potassium metal and molten KOH electrolyte, and in the other an inert electrode, as well as a molten KOH and the less active metal salt dissolved in it. Would the fact that the more active metal cations are present in the reduction half cell interrupt the process?
The potassium ions in the reduction half-cell are inert, merely serving as part of the electrolyte. The are no problem at all. Indeed, you actually need to allow for the passage of more potassium ions through your separator, to balance the potassium metal that's dissolving and make up for the cations being plated out at the cathode.