Jesus was a Jew by religion and ethnicity. There was no such thing as a Muslim per se at the time. Muslims will sometimes say Jesus and other Biblical prophets, like Noah, Isaiah, before Islam were Muslims. The idea that all prophets are Muslim doesn't mean that it's believed they all practiced Islam in the way of Mohammed and his descendants. It's more of a mindset, a relationship with God, a recognition of God. Because to Muslims, Islam is the only true religion no matter when people starting calling themselves Muslims. So everyone following, or submitting to, the true God since the beginning of the world were Muslims. Just like many Jews consider Abraham to have been the first Jew, but Judaism was not born until generations later. And like Jesus, Muslims consider Abraham a Muslim. (I consider him an American scientist, of course.) Even Adam is seen as a Muslim. There's a saying that people don't "convert" to Islam, they "revert" to it because we're all born Muslim.
It’s not believed that God told Muhammad to start a new religion. It's believed that God just gave Muhammad some new revelations, as he did Abraham, Moses, and Jesus before. It's just that Muslims believe those old revelations, the Old and New Testaments, had been changed and corrupted. Also, the Quran laid down some different rules, so they couldn't just add the Quran to the Bible and call themselves Jews or Christians. They had to distinguish themselves from the ones who followed the old or corrupted rules; hence, they came up with Islam.
Each Prophet sent before Muhammad was sent unto a particular nation or tribe. For example, Moses was sent unto the Israelites, Jesus unto the Jews. However, Muhammad is believed to have been sent unto the whole of mankind, and not just to the Arabs. The world had changed by the 7th Century. Unlike Biblical times, the world was becoming more of a global village, with ppl from one nation interacting with those around the world. New rules were needed. New revelations. According to Islam, the message brought by one Prophet replaces the laws brought by the Prophet before him. The people who lived before the coming of the Prophet of Islam should either have believed in the prophet of their time or in the absence of a prophet, they should have believed in the worship of one God alone. But those who live after the coming of Muhammad must believe in Islam, if they hear about it. Hence, the Quran and the need to believe in it to be a true Muslim. But those people in the past who were following God's true word were following the same thing. So they can be thought of as Muslims, or Muslims can be thought of as true Jews, if you want.
It's all just one of the ways a religion tries to lay claim to everything and is nothing more than brainwashing nonsense.