How should I handle the wiring if my old thermostat had two C or C1 wires?

If your old thermostat had two C or C1 wires, wrap each wire individually with electrical tape and do not connect them to the thermostat. Only a single C or C1 wire should be attached to the C terminal. (Page 2)

From the official Honeywell RTH5160D1003 manual, page 2

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