Firstly, the opposition to Jews is not a racial issue. So the fact that Moses and Jesus (peace be upon them) were racially Jewish is not relevant. In fact, one of Prophet Muhammad's (peace be upon him) wives was Jewish and at least one of his Companions was a Jewish rabbi prior to his coming to Islam. And to this day, there are many Muslims of Jewish ancestry, some of them embracing Islam in Israel. So race is not the issue.
Secondly, history will note that from the earliest days of Islam to when Muslims controlled Palestine and Spain, there has been evidence of peaceful coexistence between Muslims and Jews, unless there was something done to undermine that peace. So even though our religions differ, if Jews live within the Muslim state they are not to be harmed or persecuted.
However there is a religious basis for opposition. Muslims believe in and accept all the Prophets and Jews, for the most part, don't accept Jesus and Muhammad (peace be upon them) and have killed or attempted to kill Prophets, which is also evident in the Old and New Testament. There is also that which was done of changing the religion that had been given to them by Moses, which is alluded to often in the New Testament. But the Muslim simply says, "To you be your religion, to me be mine."
From the reasons why many Muslims, Christians, Jews and others are opposed to the state of Israel is that there are many injustices that are committed against the Palestinian people, whose land was stolen from them. It is similar to the subjugation of Native Americans and the theft of their land in North American history, or other colonization atrocities that occurred in Africa and other parts of the world. The real question is: Why are so many Jews and Israel opposed to Muslims and Palestines?