Mohammed tried to convince the Jews that he was their promised Messiah, but they didn't believe him. Jews became the hated ones. Jews rejected Mohammed and they quickly felt his wrath. This blind hatred continues to this day. While Islamics hate the Jews, they don't see the Jews as a collective threat to Islam. Jews are just used for target practice. The war with the Jews is just a prelude for what is to come.
Christians, however, were a lost cause right from the start. Christians had already accepted Jesus as the promised Messiah long before Mohammed was even born. History told Mohammed that Christians were a stubborn bunch. They had been fed to lions, tortured, crucified, beaten, and still, Christianity thrived and grew. Even the powerful Romans could not stop them.
Islamic hatred is directed right at the group of people that Mohammed knew would be the people to stand up to Islam and defeat his followers someday: The followers of Jesus Christ.