Answered by Shaykh Faraz Rabbani
I had heard that the urine of babies who are exclusively breast fed is considered tahir. is this accurate?
In the Hanafi school, all urine is filthy (najis), even that of babies. The Shafi`is consider the urine of male babies before they start eating lesser filth, and have particular rulings for it.
The difference arises from the difference in interpreting the Prophet’s command (Allah bless him & give him peace) to “sprinkle water” over a baby’s urine. The Hanafis interpreted this, because of linguistic and legal considerations, as meaning “wash lightly,” whereas the Shafi`is interpreted it as more literally. [Fath al-Qadir, I`lam al-Anam]
Note, however, that an area of 5 cm in diameter or less of filth is excused, such that one’s prayer is valid even with it, though it is recommended to remove it when reasonably possible. All filth on one’s body or clothes is considered together for this. This is useful for those with babies.
As for the fiqh of baby vomit: The fiqh of baby vomit
And Allah knows best.