Of course Conservatives disagree about what is the 'natural' order. For example the Jacobites thought it was natural for Britain to be a Catholic country, and the Tories thought it was natural to have an established 'Church of England'.
Conservatism can be relatively benign, depending on what they claim is 'natural'. So-called paternalistic or one-nation conservatives claim that the natural order is one of mutual social obligation, albeit organised as a hierarchy.
The danger is that conservatism can collapse into equating 'the natural order' with raw capability. So, if I am capable of bombing your country into submission, then it is 'natural', and therefore it is the right thing to do. If I am capable of using the mass media to persuade you of an untruth, then this is the natural and right thing to do. This is what Fascism is. (By this definition I think Stalin for instance was a fascist.)
I think that neo-cons (so called) are also fascist. They (believed they) could invade Iraq and take what they wanted, ergo this was the right and natural course. They don't believe in Creationism but they think it is part of the natural order that the 'masses' are controlled by convenient myths. A few weeks ago I quoted Niall Ferguson arguing that race isn't real but racism is natural. This is all part of a consistent overall approach.
I think it is important to realise that a sophisticated fascist believes that general happiness and well-being will arise from this approach. He believes that resisting the natural progress of the strong will be bad for everyone, and that collateral damage is a price that has to be paid. Thus the neo-cons take actions that we think are immoral and cynical. They think it is the natural and right thing to do.