What is the ruling on washing clothes in a washing machine used by those whose clothes come into contact with dogs, knowing the Prophet’s — may Allah’s prayers and peace be upon him — hadith about a dog licking a vessel, which necessitates washing it seven times, one of which is with earth? And is the washing machine considered impure?

The default state of things is purity until impurity is proven with certainty, according to Ibn 'Uthaymeen's saying: "If there is doubt about thet impurity of something pure, then it remains pure." Therefore, the clothes of those who touch dogs are considered pure until their impurity is proven with certainty. Consequently, washing your clothes with theirs or after them in the same washing machine does not render them impure.