Charmed is not the same as it was in previous editions.
Charmed (PHB p. 290)
- A charmed creature can’t Attack the charmer or target the charmer with harmful Abilities or magical effects.
- The charmer has advantage on any ability check to interact socially with the creature.
Nothing prevents a charmed creature from:
- Casting Dispel Magic (or any other spell) on themselves
- Fleeing the creature that charmed them
- Attacking the allies of the creature that charmed them
- Warning their own allies about the Charm effect
- Putting their hands over their ears and going "Lalalalalala"
Note though, that the Cambion's Charm ability does require you to follow their spoken commands, so if he had commanded you to do something that would prevent your rage, or explicitly told you not to rage, you would not be able to.
Combining this with Adam's answer regarding the Path of the Berserker Barbarian's level 6 feature Mindless Rage clearing a Charm effect, yes a Barbarian can use Mindless Rage to ignore the Charm effect while raging.
Note: A regular rage effect does NOT automatically ignore the Charm effect, at the time of this writing, only Path of the Berserker Barbarians of 6th level or higher may ignore the effects of a Charm of Fear effect while raging