Is it permissible to work in a restaurant that serves pork and alcohol, knowing that the worker washes the dishes in which these forbidden items are placed? And is pork considered similar to alcohol in terms of the prohibition of selling and serving it?

The prohibition of pork is definitive. Working in restaurants that sell pork and alcohol is unlawful (haram), especially directly serving alcohol, carrying it, manufacturing it, or trading in it, and similarly for pork. A curse was mentioned for the one who drinks alcohol, carries it, and sells it. No similar text was mentioned concerning pork, but the ruling of the prohibition of cooking it, carrying it for those who eat it, trading in it, consuming its price, or sitting at its table without disapproval can be inferred from the Almighty's saying: "And do not cooperate in sin and aggression," and from the prohibition of selling alcohol, carrion, pork, and idols.