How does it affect the treatment of a mathematician's results, if that mathematician was a Nazi?
I think there is no academic issue here. 


  The problem with Vahlen, as you may have guessed by the title, is that he was about as much of a Nazi as a person could be. He was in the SA, the SS, accused brilliant Jews of plagiarizing Aryans, helped the Third Reich expunge Jews from the scientific community, etc. He even supported the Nazi party before its infamous rise to popularity.


I looked into Theodor Vahlen, and I agree that he was a morally reprehensible individual.  But this is irrelevant to a discussion of his work: he proved the theorems that he proved whether he was good, bad, or whatever.  As is well known, the Unabomber is a published mathematician.  His six papers have eight citations on MathSciNet, three of which came long after his capture, e.g. see here.  (Though I do not know for sure that the author of this paper was aware that the T.J. Kaczynski whose work is cited is the Unabomber, it seems likely: the author is an American, and among Americans this name is well known to say the least.)    


  I was wondering what the likelihood is that his results were neglected due to this political misfortune. I was also wondering if people know of similar instances, particularly in mathematics. It seems like whenever I look up the politics of a respectable mathematician, they are either nonexistent, or equally respectable. I don't know if we tend to discredit people like this, or if people like this tend to not produce good results, or what.


In my opinion this is unlikely.  There are very famous mathematicians who were, to lesser or greater extents, participaters in the Nazi movement.  Perhaps Ludwig Bieberbach and Oswald Teichmuller are the two leading examples: these are household names in mathematics, and that they were intimately (and reprehensibly) involved in the Nazi movement is also very well known.  (For that matter, I am not convinced that Vahlen's work is so little known.  It is described in the wikipedia article linked to above, for instance.)

In my personal opinion, it is worth knowing when a mathematician (or other academic) has done reprehensible things in their personal life.  Some years ago I compiled a list of "greatest mathematicians" on MathOverflow: I limited myself to choosing at most one mathematician born in a given year, but in some cases I included "honorable mentions."  When I got to Teichmuller, I did not want to use the word "honorable" to describe him, so I wrote "dis/honorable mention."  That was a personal decision (and by the way, I am partially of Jewish descent, so it is really not for me to forgive or forget such things).  But I included him on the list anyway: that he was a terrible person does not influence his mathematics one way or another.  


  I'd like to just use a big-ol' script V for the Vahlen matrices (which I have not seen in any papers thus far) and move on, 


There is no problem with this.


  but I don't want even an iota of a suspicion of being sympathetic to this man's priorities. 


We don't endorse the life of Teichmuller when we talk about Teichmuller space or Bieberbach when we talk about Bieberbach's Conjecture.  We credit them with their work, as we must.


  It would also be hilarious to just use a swastika, but that joke might not be funny to some people (understandably).


I am not laughing at all.  Please do not do this.

Finally, you can read much more about mathematics in Nazi Germany from this book.  Again, I think it is good to know these things.