For the record the line "you would make a convincing Nazi" I took it as Kirk in that uniform looks scary and tough, that he would fool them. Not that Kirk is really anything like a Nazi.
We were talking about Hogan's Heroes in the other thread and I remember similar lines being used in that series when the characters went undercover.
I think this is the case of being offended too easily. Being Jewish myself I definitely do not take the actual Holocaust lightly but the episode wasn't about concentration and death camps.
Now as for the episode itself I can take it or leave it. Not really a big fan of the alternative world episodes and I don't think this one said or did anything all that interesting.
Looking at his comment to Yeoman Rand at the end of The Enemy Within, that the opposite Kirk (who attacked her) had some interesting qualities
Now this line bothers me as it does take attempted rape too lightly and makes a joke of it.