Aah… the dangers of medical advice over the internet. it is true that use of iodine while breastfeeding poses a very small risk to the infant, especially those under 1 month. older infants have a larger and more robust thyroid, so there is basically no risk of thyroid undergrowth in a child with excess iodine in their diet if they are older or bigger.
in reality, the risk is minimal, especially as you will be dabbing a tiny amount on a small area. it can be more of a problem if you use it on, say, a square foot of skin, as i have done in the past for road rash… iodine is absorbed through the skin to a small degree, and can therefore end up in the milk. but it’s generally not a real concern except for long term large use, and if your baby is a month or less, or 5kg or less.
neosporin use is not without its own problems either, such as the generation of resistant bacteria from repeated low dose exposure, though this is admittedly rare.