Can using a non Apple USB cable damage an iPhone?
They are generally safe to use.  And they don't have a chip (at least the ones I've used).

The charger itself may regulate the current, but the cable itself doesn't.  I've used a multitude of cables from a multitude of vendors over the years and I've never had a problem with damaging devices.   Build quality is a different matter.  Too cheap, and the cables inside can break.   Rare but does/can happen.