Very slim, to the point of non-existence.
What little influence the KKK has these days is almost completely open. People in the USA don't really have much of a problem speaking their minds, even and perhaps mainly when it involves controversial politics. There would be little point in infiltrating.
As for Nazi influence... to be frank, I think many of their values have been openly incorporated in the last few decades already, although there is considerable internal resistance and not a little self-denial as well. People these days have only a vague, fairly romanticized (or perhaps degenerated) idea of what exactly the Nazis were and why they had to be stopped.
Which, far as I can see, is because they were far too nationalistic and far too militaristic for anyone's good. Alas, people everywhere hesitate very little in following their example on these crucial fields these days.
However, I must say that I am having a hard time understanding the picture you are presenting. It does not look just unlikely to correspond to reality; it looks a little ill-informed about the nature and goals of the organizations you mention.
For all that it deserves criticism, US police is fairly well watched, both by other organizations (and rival police forces, even), by the media and even by the population itself. Violent racists do exist in it, but they are if anything too openly visible.
I am left wondering if there is some mistranslation here:
That explains the killings of many invaders by the police/army.
I'm honestly not sure what this is supposed to mean. Armies are usually expected to kill invaders, so there is not much of a need of an explanation for them. And police is expected not to use lethal force except in self-defense or when left with no other choices for the protection of others. Besides, police officers don't really deal with "invaders" in any regular basis. So maybe invaders is not quite the word you meant to use?
