I installed the terminators but want to follow up on the reason.
What "cable" do you refer to when it's an active splitter device?
I can see the impedance issue if using a passive divider but am less clear on the benefit in a active system.
An active multicoupler ("antenna distributor", "active splitter", etc.) is merely a passive splitter network with a low noise pre-amp feeding the splitter's input (though better designs will also incorporate bandpass filtering).
The passive splitter network itself is designed around all ports being terminated by the appropriate impedance load (50 ohms in the case of RF). When a port has improper termination, or no termination, energy is reflected back into the network to both the summing (common) port as well to the other output ports. An unterminated port causes a change in isolation between ports by changing the overall internal impedance of the network.
Reflecting energy back into the summing port will back feed into the output of the LNA possibly causing IM mixing, saturation, and occasionally even damage in cheaper units.
That said, the better wireless microphone multicouplers are rather forgiving about unterminated ports, and that alone will not cause any significant detrimental effects. But coupled with other problems the wireless system might be experiencing, unterminated ports could exacerbate problems. Given how cheap this proper RF practice is, it's not worth ignoring.
Mini-Circuits has a rather good
application note on passive splitter networks.