Why? Why would it be out-of-place to use the word 'radical' to characterize violent extremism in the name of one religion (the majoritarian, white-person religion, we should note), but acceptable, commendable even, in the case of another? Why can we not use 'radical Christianity' to characterize the horrendous acts committed at the behest of the reprehensible 'Army of God', but every instance of violence in the name of the Qur'an must be characterized as 'radical Islam'?
The answer is not complicated, and it has to do with the meaning of the word 'radical.' The word 'radical' originates from the Latin word radix, meaning 'root.' (For the etymology nerd in you, it's connected to the word 'radish', an edible root popular on salads). 'Radical politics' indicates a political philosophy that seeks to transform the roots of the political structure, 'radical change' means a fundamental change that goes to the root, etc.
When we use the word 'radical' to characterize something, we are indicating that it encapsulates the essence of whatever we are talking about. So when 'freedom-loving Americans' (to use Bauer's terms) refuse the words 'radical Christianity' to characterize violent acts committed in the name of the Christian faith, it is because they know that such an equivocation would mean that, at bottom, Christianity really is, essentially a violent religion. And they naturally reject this. Christianity, they say, is a religion of love and forgiveness, extending even to one's enemies. So 'radical Christianity', they argue, means really living out this impossible love that Jesus preached - faithfully living out the essential nature of Christian teaching. Anyone who commits violent acts in the name of Christian teaching, they would say, is not really Christian at all. (Although the aforementioned 'Army of God' upholds such people as 'American heroes'.)
This is precisely the reason that most Muslims reject the language of 'radical Islam' applied to the purveyors of violent jihadism. But here's the rub: if the American right recognizes this in the case of Christianity, then it stands to reason that they equally recognize the implications when the word 'radical' is used to characterize violence in the name of Islam as well. That is, they recognize that to use 'radical Islam' as a synonym for violent jihadism, is to in the same breath suggest that, at bottom, Islam really is, essentially, violent. The right likes the word 'radical' in the case of Islam, and rejects it in the case of Christianity, for the very same reason - as they see it, violence really does essentially characterize Islam, but is mere aberration and inauthenticity in the case of Christianity. For them, a peaceful Muslim, is the exception, not the rule. This is why the right constantly demands that Muslim communities must denounce violent jihadism, willfully ignoring the fact that they already do. This deliberately ignorant insistence suggests to their listeners a dangerous, quiet acquiescence on the part of Muslims with acts of violence carried out in the name of Islam - this was the prejudice into which Donald Trump tapped when he decried the non-existent 'thousands' of supporters in New Jersey who cheered as the twin towers fell.
This is problem - the hidden subtext behind the language of 'radical Islam.' It is, purely and simply, dog-whistle Islamophobia, executed in order to appeal to the very worst parts of human nature.