Also, does changing a baby's diaper invalidate wudu?
Praise be to Allaah.
We would like to congratulate you and offer praise to Allaah for the blessings He has bestowed upon you by guiding you to the Straight Path. We ask Him to help us and you to be steadfast in adhering to this religion.
You do not have to use soap at all when doing wudoo. The word wash which you have read in the books you refer to does not mean using soap or any other kind of cleanser.
With regard to changing a babys diaper, if you mean the act of changing itself, this does not affect the validity of one's wudoo.
Shaykh Ibn Uthaymeen (may Allaah preserve him) said:
Washing the hands and face with soap when doing wudoo is not prescribed in shareeah. On the contrary, it is a kind of obstinate and excessive zeal. It was reported that the Prophet (peace and blessings of Allaah be upon him) said: Those who are obstinate and excessively zealous are doomed. He said it three times.
If there is some kind of dirt on the hands that can only be removed by using soap or some other cleanser, there is nothing wrong with using it in this case, but under ordinary circumstances, using soap when doing wudoo is a kind of excessive zeal and bidah (innovation), so it should not be used. (Fataawaa Islamiyyah, 1/223)
If you mean that it involves touching something that is naajis (impure, i.e. the babys urine and stools), this does not affect your wudoo either, because there is no connection between touching something naajis and the validity of ones wudoo. It has been reported that there is scholarly consensus on this point, as stated in the book Al-Awsat by Ibn al-Mundhir (1/203). All one has to do is wash one's hands to get rid of any naajis material.
If you mean that it involves touching the childs private parts, whether the child is a boy or a girl, in the case of a child under the age of two years, the rulings on awrah (that which is to be covered) do not apply, as the scholars have stated, so if you touch them, this does not affect your wudoo. And Allaah knows best.
Sheikh Muhammed Salih Al-Munajjid