You can choose not to support Zionism. But if you actively believe "Jews should not have a homeland" that is anti-semetic.
Saying the same about Jews should be looked at similarly, and yes there is quite an overlap between anti zionism and anti semitism.
Also - Zionism means different things to different people; Bernie Sanders' Zionism (yes, he is a Zionist) isn't the same as Benjamin's Netanyahu.
But simply outright rejecting Jews right to live in ANY borders in that area seems to me quite hard to justify. It may not be racist in and itself but it has big (probably bad) consequences for the jews living there if it's ever realized, and it is an idea that is loved by many people who are anti semitic (either muslims, extreme right or extreme left supporters).