Will cutting out sugar or flour while breastfeeding decrease my milk supply?

I have read in a few places that a low carb diet it will dramatically decrease milk supply. For example, Diet Doctor recommends not doing a healthy low carb intake while breast feeding, as milk supply will go down. This makes me nervous to cut flour and sugar (and serves as an excuse / justification to keep eating them when I’m uncomfortable), as I am exclusively breast feeding a 6 month old.