A hot take on current events

 In a recent tragedy, two Israeli embassy employees were shot after an event in Washington, D.C. Aside from the crazies who justify murder and defend it as a viable expression of resistance to actions of a foreign government, people see the murders as wrong. I see the murders as wrong. So let's not get the wrong idea about what I'm about to explore.

One thing which is being thrown around is the claim that the murders were not just an attack on Israel (seeing the 2 employees as proxies) but that they were anti-Semitic. I have been wrestling with that and I'll explain why:

the attacker targeted Israelis (though even this is unknown and until we know how he chose his targets, we won't know his motivation explicitly; we will just be inferring)

the attacker recited slogans that relate to Israel, Gaza and the mideast. He said and did nothing which invoked religion.

one of the victims was not, according to Jewish law, Jewish. Did the shooter know or care about his religion? Does it matter if the attacker THOUGHT he was Jewish? Or thought that he was Jewish according to Judaism (does killing obvious non-Jews coming out of a synagogue make the attack anti-Semitic?) The victim was only patrilineally Jewish -- who determines religion to find out if the attack was religiously motivated?

the attacker attacked outside of a Jewish museum and after an event that was sponsored by a Jewish group. Was it just that assumption of Jewishness because of context?

I just have questions -- I don't know whether this is a prime example of the difference between pure anti-Zionism and anti-Semitism, or where this is an example of how the two are conflated accurately.