Trump has no filters and speaks informally, as if he's having a conversation with his audience rather than reciting a scripted speech. If you ignore the content of what he says, he sounds honest and guileless. It is a marked contrast with the highly scripted speeches that so many politicians deliver. Even if every word they utter is true, they sound false.
One of the reasons that the "Crooked Hillary" meme resonated with so many people is that Clinton is not the best speaker; her tone is quite stiff. For people who didn't like her anyway, it's easy to interpret that delivery as false and insincere. For people who DO like her, we simply recognize that's not her strong suit and take the words at face value.
People respond strongly to tone far more than is general recognized. Tone directly touches the emotions, whereas content has to route through the brain and those messages arrive later (if at all, for some people). I don't think there's any getting around this, and my personal solution is to consider "performance" to be a critical job qualification for president. It's not a "nice to have", it's a "must have" in terms of winning over the electorate.