When you figure out how to tell a fanatic they are a fanatic without a backlash, with any success, you should let the UN know, pretty sure they want to figure that out.

Do you not see how condescending that is? You assume because someone is militant about something they are ignorant or need to be re-educated to be more mainstream. That totally ignores the fact that they don't WANT to be moderate. They don't think there is a middle ground. So be offended if you want to be, but it won't change their minds.
The term "Breastfeeding Nazi" doesn't belittle all the women promoting breastfeeding, it only belittles those who take offence to the term. It only does harm to the cause if you can't distinguish between the extremists and the supporters. It is like taking offence to a Palestinian extremist who just blew up a cafe a "terrorist" because you are also a Palestinian. He is a terrorist, but that doesn't change your message as a Palestinian. Intelligent people know the difference. If you want to appeal to the lowest common denominator then you will spend your life debating semantics and trying to explain the difference between night and day because they just won't get it.
So you are right, the people the term is aimed at won't care, they will wear it with pride, and the ones who it isn't aimed at take offence to it and let it control their agenda. They shouldn't.
It is a throw-away term, useless as it only makes sense to those who already have a line in the debate. Either you are a formula feeder who agrees with its sentiment or you are a breastfeeding advocate who takes it personally. Either way though, they label isn't changing anything as those it is assigned to don't see the negativity behind it.

The sooner everyone stops trying to be so PC about every little thing and being so tolerant of everyone's "choices" the better off we will be.