It seems that it used to be normal to castrate some boys for the purpose of making them servants....when did practice start seeming immoral to people and when did they stop doing it? Obviously we don't make mutilate the genitalia of little boys today...
Do you have a particular culture in mind? The very last eunuchs I know about that would have (likely) been castrated expressly for service/enslavement would have been in the 1930s-1940s, in Ethiopia, for the Middle East. The last Chinese eunuchs would have been castrated maybe around 1915. The ending of castrated slaves in the Middle East (there's still some alive) would be tied to the end of the Ottoman Empire, and all the various 20th century abolitions in that area of the world. The ending of the Chinese eunuchs was tied to the end of the Qing dynasty. Sadly morals had basically nothing to do with the end of eunuch servants.