Opposition to Zionism is very different from anti-Semitism and many Jewish people are also opposed to Zionism. The Jewish people certainly have a right to exist and the right to a homeland; but the Palestinians have those rights, too.
Here is a short history of the Israel/Palestine conflict:
You’ll notice that the basis of the current conflict is the colonialism and meddling of the British empire. Here’s another one, which brings up the same point.
And here’s a music video that portrays the complete history of the land we now call Israel and/or Palestine:
An interesting detail of this whole thing is that conservative Americans support Israel mostly because they want the Jewish people to rebuild “the temple” which conservative Christians believe is necessary for the end of the world to begin. Yes, they are supporting Israel because they want the Apocalypse; I think that really cements the perfection of the above music video.