So, is support for Palestinian rights or criticism of Zionism still "antisemitic" and "racist"?

No.

Ironically, conflating anti-Zionism can itself be antisemitic.

Calling all criticism of Israel antisemitic is a smokescreen to avoid any legitimate criticism of or evaluation of Israel's actions, and it is pushed by the Israel lobby in Western nations.

There's so much division in the Western World over conflict in the Middle East when a majority of them have no idea what is going on, except for what their favourite media outlet decides to pump out one side of the story of.