All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
According to the sound opinion of the scholars, a non-Muslim's impurity is moral, not physical. Consequently, if their clothes are not smeared with actual impurity, they are pure just like a Muslim's clothes which are not afflicted with impurity. Nevertheless, if one thinks that their clothes are mostly impure because they are not keen to avoid being touched with impurity, it is better to avoid such clothes until they are purified. In the case in question, there is no doubt that the maid’s clothes become free of impurity through the process that the questioner mentioned and it is permissible to use the same machine for washing your clothes.
Allaah Knows best.