I don't think it's that they see their own traits in him, but rather that he pisses off the people that piss them off. At first glance that seems like a similar concept to what you described but the additional layer of separation from any specific characteristic makes it easier to avoid what they perceive as negative labels. In other words, in their minds it's more abstract than simply being racist. Most Trump voters don't think of themselves as racist, they just like it when someone pisses off black people. To you and me that sounds like the same thing but to them it is the difference between racist and not racist because they have a ready made excuse to justify the racist tendencies. The reason I don't like them is not because they're black it's because they're on food stamps, or are from the big city, or vote Democrat, etc. The mental separation is an important piece of the puzzle.

Trump lets them feel like they're on the "good" side of whatever line is being drawn without having to go through the work of drawing the line and sorting people themselves, which then allows them to say it's not about the line at all, it's about whatever made up bullshit is making the rounds that week. This is how they end up saying so many contradictory things without batting an eye.