Can a Muslim woman breastfeed a Christian child, and likewise can a Christian woman breastfeed a Muslim child? What is the Islamic ruling if breastfeeding takes place?

Fatwa, posted 4.22.2010, from Egypt, in:
Religious Authority: 
Muhammad Saalih al-Munajjid
Fatwa Question or Essay Title: 
May a Muslim woman breastfeed a Christian child, and likewise may a Christian woman breastfeed a Muslim child?
Websites and Institutions: 
Islam Online

It is very important to note that there is nothing wrong with a Muslim woman breastfeeding a Christian child or a Christian woman breastfeeding a Muslim Child. In this regard, Shaikh M. S. Al-Munajjid, a prominent Saudi Muslim lecturer and author, states the following:

“It is permissible for a Muslim woman to breastfeed a Christian child and it is permissible for a Christian woman to breastfeed a Muslim child, because the basic principle is that it is permitted, and there is no evidence to the contrary. This is a form of kind treatment and Allah has decreed kind treatment in all things. It is proven that the Prophet (peace and blessings be upon him) said: “In every living being there is a reward.”

If breastfeeding takes place, then the Islamic ruling on each of them is not altered because of the breastfeeding. Whoever was a Muslim before breastfeeding remains a Muslim afterwards and whoever was a Christian before breastfeeding likewise remains a Christian.”