Producing political apathy and learned helplessness is an explicit purpose of the "Flood the zone" propaganda strategy.

It's a serious requirement for despots. You don't need a large and supportive group. You don't need 80% of the population expressing support for your acts.

All you need is like 20% of the population absolutely Ride-Or-Die levels of support for you, willing to do violence and hate on your behalf, and everyone else just kind of apathetic, unsure, or oppressed enough to stay down.