Of course they think that.
It's not that they adore him despite all that, they adore him BECAUSE of it.
Dictators appeal to a certain demographic, and they take hold of power when that demographic feels their futures - economic, standard of living, cultural, etc - are under a prolonged threat or downward spiral.
That Mexican taking the only jobs they're qualified for (not that they would work in them)?
GONE!
That trailer park they have to move to even worse than the one ma kicked them out of?
GONE!
That muscular bare chested sweat gleaming gent in a tutu they fear might be at the urinal next to them staring at their little willie?
GONE!
People darker toned than them getting elected to higher office?
GONE!
Them city folks getting a share of the pie only they should get because the South got destroyed a century and a half ago during the War of Northern Aggression?
GONE!
Then you have the elitists who are the only ones who will benefit while the dregs get to bathe for joy in mud. They'll back him and do what they can to keep him in power because the corrupt benefit from the corrupt.
This is what happens in all Autocracies - their roots, rise, takeover, establishment, and sucking dry of a rotting corpse.