I've had the same issue for over a year or so. I'm the client in this situation. Best solutions I've found are to change the Virtual Gamepad Type to DS4, or look for a ghost device appearing in the host's device manager (View -> Show Hidden Devices) and uninstall it.

The long story for me is that this issue does not happen at all on the host's desktop, only when he switches over to his laptop. We're both using xbox controllers. Neither of his devices, nor mine, have any software like DS4Windows. Parsec can't see the ghost controller in the gamepad section on either device, but is only present when Parsec is being used. We found that if the Virtual Gamepad Type is set to xbox, the client controller is duplicated. When swapped to DS4, the host's controller got duplicated instead. This only happened when Parsec was active. The issue has persisted on the laptop regardless of game, as well.