The issue lies in the fact that some believe (including orthodox Jews) that the Zionist State of Israel shouldn't exist because it is not in the Torah hence it is against the teaching of Judaism and what it is to be a religious Jew. However, the alternative argument is, why shouldn't the Jewish people have a state of their own? The Torah does say that Jews should not return to Israel until the return of the Messiah, but like many countries nowadays Israel also has a secular society.
I don't think this is a fair question. Discussions on this site have actually led me to spend a considerable amount of time researching the topic- even just to determine when anti-zionism is anti-semetic. There are times it is. It absolutely is. And, there are debates even in the Jewish community about this.
A while back I found a fantastic article that outlined the differences and how difficult it can be to spot things- seriously minor linguistic changes can shift something to make it anti-semetic, even if that isn't the speaker's intent.
If a person uses Zionism and Judaism as interchangeable terms, then that is a problem. If a person uses language that suggests all Jewish people are zionists, that could also become a problem. And, sometimes, the language used is gray- unclear whether the person is splitting the two. That is also a problem.
But, let's just say, for argument's sake, that someone takes offense to a comment that really is not anti-semetic, but is anti-zionist. Well, I don't think it's much different than what we see with lots of other demographic groups. We have republicans here who feel attacked when someone goes after some republicans. We have democrats who do the same. It happens with the right and the left. Pro-Trump; anti-Trump, etc. In my opinion, what it boils down to is how much that particular individual personally identifies with the group in question. i.e. If I'm a Trump supporter who has made supporting Trump a huge part of my life- maybe I volunteered for his election campaign and attended his rallies- then I personally identify as a Trump supporter. It is part of the fabric of me. If someone starts bashing even some Trump supporters, I'm going to feel like they're attacking me.
I also think that the Jewish community has had far more than its share of discrimination and hatred pointed in its direction. Even in Charlottesville, the neo-nazis were chanting anti-semetic phrases. Ergo, we're not talking about a group that was attacked generations ago. We're talking about a group that is still being attacked and hated today over their religion. It is almost impossible for that not to impact people who follow the faith. If they're constantly under attack, they're going to be on high alert. In some cases, crap like that can induce PTSD. This is true of ALL groups. The more your group is under attack and the more often you're subjected to it, or the more drastic the attacks are, the more it will impact the people in that group.
I actually had to write a research paper over the weekend for my abnormal psychology class outlining how a well-known tragedy could impact people of specific groups. I personally chose to write about Charlotesville and how that could have impacted the mental health of African Americans (there is a scientific/ medical basis for it), but I could have just as easily highlighted how that one event could have impacted the Jewish Community or the LGBT community. The point being, these occurrences shape who we are and how we function.
I was out with a friend last week and she happens to be a latina. Her son snuck out one night and was gone until early morning. She recounted the lecture she gave him to me. Part of it was, "Honey, you're brown. You cannot be out in the middle of the night. It's not safe." I have heard similar sentiments from my black friends- that they have been coached to be extra cautious because being out can put a target on your back even when you're not doing anything wrong.
The same thing happens in the Jewish community too. It happens in all communities that have been under attack. My friend wasn't wrong. Her son would be less safe than mine would, purely because they're different colors. At the same time, she was conditioning him. She was putting fear in him. That fear may keep him safer, but the more he hears the message "You're not safe because you're brown," the more afraid, wary, and vigilant he will become. I don't have a solution for that. Again, I don't think she was wrong and that's incredibly sad. But, if you know anything about psychological conditioning, then you know she's programming him to be reactive. Or maybe proactive. Either way, it's going to impact the way he sees the world and interacts with it.
I am betting that if you put some thought into it, you'll probably be able to identify groups you belong to that have parallels here too.
So, no... it's not fair to say these people have an "agenda." They are just people subject to the human condition, same as you and me.
As for the flip side, people who see them as the same when they're not the same (which your question could also mean, though I don't think it does), I can only attribute it to lack of knowledge on the subject.
Depends what you mean by "anti Zionism". If it means denial of Israel's right to exist as a Jewish state, then it is antisemitic. If it means criticism of specific actions done by the Israeli government, such as settlement building, then not necessarily. But even in the second sense, it can slide into antisemitism if it becomes an obsession.
