Mother’s milk is taahir (pure) according to according to the consensus of the scholars, may Allah have mercy on them.
It says in Haashiyat al-Qalyoobi (may Allah have mercy on him), 1/81:
The milk of any animal whose flesh may be eaten is taahir (pure). Allah, may He be exalted, says (interpretation of the meaning): “pure milk; palatable to the drinkers” [an-Nahl 16:66]. The same applies to human milk, because it is not appropriate, due to its honoured status, that it should be of impure (najis) in origin and nature. End quote.
An-Nawawi (may Allah have mercy on him) said:
Human milk is taahir (pure) according to our madhhab [i.e., the madhhab of Imam ash-Shaafa‘i], and this is the definitive view of our companions except the author of al-Haawi, who narrated from al-Anmaati that it is impure and it is only permissible for infants to drink it because of necessity.
But this is an invalid view; rather it is an obvious mistake, and things like this are narrated so as to refute them. Shaykh Abu Haamid narrated that there is consensus among the Muslims that it is taahir.
End quote from Sharh al-Muhadhdhab, 2/587
Al-Mardaawi (may Allah have mercy on him):
Milk of humans and animals that may be eaten is taahir, and there is no scholarly conflict on this point.
End quote from al-Insaaf, 1/343
Once it is proven that it is taahir, it is permissible to pray wearing clothes that have got milk on them, even if they have not been washed, because it is taahir, so it is like any other taahir substance.
Secretion of milk from the mother’s breast does not invalidate wudoo’. This has been explained previously in the answer to question no. 74901.
And Allah knows best.