Should one cite unethical research that may contradict one's current research? Most people are familiar with the controversy over citing Nazi medical experimentation and related unethical findings. I'm not questioning that.
Assuming that citing unethical research in order to bolster or support one's own findings is, in fact, unethical, does the situation change if the prior unethical findings may contradict, falsify, or otherwise be potentially detrimental to one's own findings?
For example, many feel that publishing this is unethical:

In this paper, we demonstrate that splines are reticulatable in six-space under the Transhalpine Coordinate System. Evil Nazi Supervillain (1941) demonstrated that a spline can exist in six-space. Assuming this to be true, our model demonstrates how such as spline can be reticulated with respect to the Transhalpine system, to wit....

Assuming that would be, in fact, unethical, would this be any different:

In this paper, we demonstrate that splines are reticulatable in six-space under the Transhalpine Coordinate System. Goody-Two-Shoes, Angel, Seraphim, Hero, Superhero, and Person-Who-Was-Mostly-Good-Except-That-He-Jaywalked-Once-When-He-Was-Eight-And-Was-Continuously-And-Justly-Punished-Throughout-His-Lifetime-For-Said-Act (1932) demonstrated that a spline can exist in six-space. Evil Nazi Supervillain (1941) obtained a contrary result in which splines cannot exist in six-space, but we only mention this because ethical requirements require that we disclose to you that we are are aware of a prior result that may affect our findings. The result was gained by attempting coordinate transformations on splines that had not granted informed consent for geometric experimentation. In this case the researcher was, like, a super bad guy and you, like, totally should ignore his findings because he was even more evil than Dr. Doom and his paper is probably full of shoddy praxis, negligent notetaking, and even outright fabrications.
Assuming that a spline can actually exist in six-space, our model demonstrates how such as spline can be reticulated with respect to the Transhalpine system, to wit....

Generally speaking, is it more ethical to cite or not cite the potentially problematic prior result?
I suppose the gist of this question is which ethical duty is paramount:

The duty to honestly account for the current state of research and disclose potential findings that may affect the current paper.
The duty to not acknowledge or use unethical research.

Could this one of the &quot;unusual circumstances&quot; mentioned in this answer?
I suppose that the Don't Cite Unethical Research rule could be clarified as actually meaning that it is unethical to benefit from prior unethical results, so a citation that does not benefit the later researcher (but in fact serves more as a disclaimer) would be allowed. Would that be more along the lines of how this would actually be handled?
Are you conflating evil people with scientific results that they achieve (by valid means)? They should not be conflated. Condemn the people and the evil acts that they do, but not any valid results obtained by honorable means. Evil monsters don't need to always act in an evil manner. 

There is, for example, a lot of both computer engineering and mathematics that was done by total racists. This was in the US and in fairly recent years. This doesn't make it invalid to use computers, nor does it invalidate the mathematics itself. 

It isn't even necessary to state that X was an evil monster otherwise when citing X. However, if you are writing about racism or other evils, then it is perfectly appropriate to point out the flaws. 

Of course, the spline research would be discredited if to do it evil acts needed to be carried out, but you don't seem to be saying that here. 

What is true is true, even if uttered by monsters. What is false is false, even if uttered by angels. 



Since the question was changed, I'll add this. If "research" has been discredited for any reason then there is no need to cite it other than as something not to be done. There is no need to cite failures to prove a theorem when you provide a proof, and there is no need to cite research that was done unethically. The results themselves are in question. 

There are a lot of ways to fail at research. Lack of ethical behavior is only one. Don't cite the failures, except as failures. 

In the case at hand, the research resulting from unethical behavior doesn't "contradict" the current work. It wasn't valid in the first place.