Why do Muslims hate Jews and Christians considering that Muslims' customs are similar to those of Jews and Christians?

It depends on the Muslim in question. Usually hatred by one group of another group has very little to do with actual differences between the group. In New Guinea, for example, the hatred between numerous tribes that look identical to unaccustomed foreigners is quite strong and their mutual feelings towards Westerners, who are much more different are much more muted. Muslim hatred for Jews and Christians comes primarily out of the political problems of history. Most recently, Christians in the Balkans and Jews in Israel revolted against the Muslims in pursuit of ethnoreligious nationalism. The Jews and Christians argue that they were second-class citizens under Islamic control and revolted in order to restore equality and the prominence of their traditions. Muslims saw it as being stabbed in the back for centuries of tolerance. These political squabbles manifest in hatreds of the ethnoreligious groups that engaged in those nationalist experiments. This then primes those Muslims who are particularly outraged when they look at the History of Islam to see a consistent message of mandated hatred where one does not exist.