Short answer: there is unlikely to be any specific rule against using the NRA as an example of a political organization, and the problem isn't even about the NRA as such; it is simply that it is an organization on one side of the culture war, and part of your post was misinterpreted as an attack against it.
Long answer: you've inadvertently painted yourself into a corner, simply by mentioning the NRA and the KKK in the same sentence. The reaction you've gotten to this no doubt feels neither fair nor logical - unfair in that (in an ideal world) it should be perfectly obvious that you were not intending to malign the NRA, but that it was simply one of the two examples of political organizations that came to mind. And it is true that what you wrote does not logically imply an accusation against the NRA.
Unfortunately, what you wrote is superficially very similar to what someone might write if they really were attempting to associate the NRA with white supremacy in the minds of the readers, and the NRA is an organization on one side of an extremely vicious culture war in the United States, which really does get attacked in this sort of underhanded way on a regular basis. This means that NRA supporters - whether actual members or just those on the same side of the culture war - are naturally hypersensitive to anything that even might be such an attack. (The rationalist community calls this "pattern-matching".)
(You should also read The Illusion of Transparency.)
Even more unfortunately, it isn't uncommon for a culture-war belligerent to "play innocent" when called on this sort of attack, so once someone has decided you're the enemy, there's no way for you to convince them otherwise. Anything you do will just be taken as further evidence of your perfidy. (And yes, sadly, the culture war really does seem to have gotten that bad.)
I'm hesitant to suggest any way to move forwards at this point. You may be better off cutting your losses, so to speak, and leaving the answer as it is; while it may not be as good as it could be, it is still a good answer.
If you think the NRA is a better example than the KKK, perhaps you could remove the KKK from the post and use the NRA and some non-threatening left-wing organization instead; but under the circumstances I'd recommend against doing so without an explicit OK from one of the moderators.
If you don't want to leave the answer the way it is, a better option might be to dump both the KKK and the NRA and try to think of another two examples. Just make sure that the chosen examples won't be objectionable if people think that you're comparing them to one another. Because they will.