What I oppose is not that the word Nazi is being applied in another context, because I can see how it could transfer in a meaningful way. I oppose "breastfeeding Nazi" because the offence is no where near what the Jews endured. It isn't an equal comparison, the passion of the militant pro-BF'ers who take it too far, still pales in comparison with the passion (is that the right word?) of Hitler to exterminate the Jews. It just isn't on the same plane.
I hear you. In my mind that is why the word is used - because it does illustrate a very clear image in the mind of just how far some people are into it. That they do take it just as seriously, iykwim.
I must admit I encounter the extreme militant mindset of many more people in the anti-circ crowd than the BF crowd. I have seen threads where people suggest in very strong terms the arrest of parents who choose to circumcise, where removal of children and the words "child abuse" are used, where the advocation of violence against those who circumcise is strong. To my mind, the phrase "intact nazi" should be applied more readily than "breastfeeding nazi", I don't often hear/see that violent response to feeding choices.

Again, though, I suppose it comes back to the (mis)use of a single word getting in the way of the issue from either direction. It is hindering the message, so it is ineffective. This doesn't mean that the people it is trying to describe are figments of the social imagination though.