There is another important aspect to Trump: he doesn't attack his own voters. As a populist he wants as large of a voter base as possible. The establishment always insists that even self-proclaimed conservative candidates distance themselves from the "radical right" deplorables, and he's refused to.

So right-wing voters get the idea he's on their side because they're like the shunned weirdo in school who nobody ever pays attention to until one day the cute girl actually smiles at them and says hi. And then the media/other politicians are like the preppy bullies who now pair the cute girl with the weirdo because she was nice to him and refused to bully him like them.

The establishment declared Trump right-wing. He never claimed to be.