First off, I don't buy the parallel between inciting terrorism and the coddling of the right - There are obvious and extreme socioeconomic and geopolitical differences at play amongst the targeted populations, which has been conveniently ignored here.
I will respond to your previous post when I get some time, but for now - I think its important to realize that principles remain constant even when details change. And the principle at work here is:
Indeed, it is the easiest of cases: It merely requires being more rigorous about the truth.
It's really that simple. You cannot lump people together just because it feels good to do so, and expect rational people to fall in line with that. Just because Fox may attempt at various times to pander to both certain elements of the far-right, and elements of the center-right and center, does not mean that they are all the same. It just means that Fox tries to draw in many different markets.
I feel a need to once more quote Confucius:
If names be not correct, language is not in accordance with the truth of things. If language be not in accordance with the truth of things, affairs cannot be carried on to success. When affairs cannot be carried on to success, proprieties and music do not flourish. When proprieties and music do not flourish, punishments will not be properly awarded. When punishments are not properly awarded, the people do not know how to move hand or foot. Therefore a superior man considers it necessary that the names he uses may be spoken appropriately, and also that what he speaks may be carried out appropriately.
What Confucius was referring to was precisely rigor in applying labels, specifically social labels. To wit: if you allow your language and thinking to become muddled and inaccurate, chaos ensues and things go to shit.
No matter how strongly someone feels about some particular issue or how much they loathe people who hold different positions than themselves, in the long run no good will come from trying to achieve your ends by invoking logical fallacies to justify misusing labels.