I'd argue that the author got the description right while getting the reason wrong.
First up a confession. I'm a cycling tragic who'd like nothing more to see the vast majority of urban transportation space allocated to walking, cycling and PT.
But cyclists do upset the 'moral order of the road'. The speed differential between car & bike is significant which causes cyclists to disrupt traffic flow. Many cyclists don't conform to road rules (I treat stop signs as give way/yields all the time). Cyclists can easily navigate through gridlock that leaves motorists fuming in rage, and they do so with a smile on their face because lets face it, its very hard to arrive anywhere bummed if you got there via a relaxing ride.
The moral order of the road, like most things in life, is reciprocity. If I'm stuck in traffic, then everyone should be. If I have to follow these rules, then everyone should. When people don't do these things, we get angry because it just isn't fair.
But what the author misses completely is why the order exists in the first place and why cyclists (often) think they can be excused from this order.
The moral order on the footpath/sidewalk/mall is completely different to the road. Watching people walk through a crowd is like looking at ants. Chaos. But ordered chaos. There are no formal rules (until one steps on the road that is) but people manage just fine thanks to common sense, social convention and lack of speed differential. Before the car, this is exactly what our roads used to be like.
Cyclists (mostly) realise that road rules were created with little regard for them. Hence they don't feel the same degree of reciprocity that motorists do (who typically don't realise road rules have little regard for the needs of cyclists). Hence animosity between two groups who have very different conceptions of fairness. If cyclists had dedicated space however, or if road rules gave equal concern to all users, then I think the animosity would be much less.
Just look at the animosity (or lack of) between motorists and PT users. Motorists can see a trade off (crowded buses, no door-to-door service) for any dedicated road space/transit lanes they may receive, hence exceptions to the 'moral order' of the road are deemed fair. Cyclist typically don't experience that trade off because cycling as a form of transport is, well, simply the efficient and awesome to get around urban environments.
The animosity then, stems from a faulty sense of reciprocity or fairness. Cyclists think they have exemptions to some motoring rules but don't seem to pay any extra costs. What motorists typically fail to realise however, is that those costs are a function of their transport choice - they get stuck in traffic simply because they are the traffic.