Are anti-Zionism and anti-Semitism the same thing?

People who are anti-Zionists are often also anti-Semites

Question: Are anti-Zionism and anti-Semitism the same thing?
Position‹3 of 3: They refer to different concepts but both are damaging
Argument1 of 3›: People who are anti-Zionists are often also anti-Semites

The same people spreading anti-Zionist thought are likely to be the same people harbouring anti-Semitic views.

The argument

Anti-Semitism and anti-Zionism functions in the same way. The two concepts may not be identical, but both go hand-in-hand. Anti-Semites are often also anti-Zionists, and anti-Zionists also often subscribe to anti-Semitic views.

Context

Racists are not the same as segregationists. But the same people who are racist are often segregationists and the segregationists are also often racists. They may not be linguistically the same, or apply to identical contexts, but the same people subscribe to both.

Premises

[P1]Anti-Semitism and anti-Zionism, while conceptually distinct, function in similar ways and frequently overlap in practice. [P2] People who hold anti-Zionist views often also hold anti-Semitic views, and vice versa. [C] Therefore, anti-Zionism and anti-Semitism refer to different concepts but both are damaging and closely linked.

Counter-arguments

This is empirically false. While racism is an essential component of segregationist thinking, anti-Semitism is not an inherent part of anti-Zionism. This is evident in the many Jews who do not subscribe to Zionism and the anti-Semites who embrace Zionism. Also, just because a group that subscribes to one view is predisposed to another view doesn't mean that both views are dangerous. If it turned out that 99% of convicted war criminals love apples, that wouldn't make apples dangerous.

Rejecting the premises

[Rejecting P2] Just because a group holds one dangerous belief, doesn't mean all that group's beliefs are dangerous.