lazy. It's the equivalent of calling someone a racist. Throw some big scary name out there to shut down debate. Nowadays, when people call someone racist, homophobe, misogynist, etc.., their definition of what constitutes a racist or misogynist is highly subjective and is very open to debate.
It basically says, "I don't want to debate you on the merits of the discussion, so I'm just going to take the lazy route, call you a misogynist, and yell a lot...very emphatically."
Too suggest that everyone and anyone who disagrees with public breastfeeding for any reason is misogynist is just lazy and lacks any kind of thought.