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This opinion is grotesque and ugly. Being Jewish is not determined by one’s opinions about the modern political nation-state of Israel.
It’s entirely possible for Jews to have a historical, cultural, or ancestral connection with Eretz Yisrael/Palestine; believe that Jews should be free to safely live as a community in Eretz Yisrael; but not think this requires a political state with a Jewish demographic majority.
Jews can believe in and support the ability of Jews to live as a community in Eretz Yisrael/Palestine while also supporting the rights of Palestinians - including those forcibly displaced in 1948 - to live in Palestine/Eretz Yisrael, with equal rights for all citizens.
People might disagree about the practicality of that, or disagree about what constitutes an ideal resolution to what is generally referred to as ‘the Israeli-Palestinian conflict’, but it doesn’t make someone *not Jewish*. 
Also: classical antisemitic stereotypes (which long predate the state of Israel) portray Jews as a disloyal 5th column undermining our countries from within, in favour of ‘international Jewry’ and so forth.
Accusing non-Israeli Jews of being “traitors” for disagreeing with you about Israel reinforces the antisemitic idea that Jews have ‘dual loyalty’. Not only is it false, it’s a wildly irresponsible idea for @Eve_Barlow to promote if she wants to fight antisemitism.
Being Jewish isn’t contingent on a particular political ideology centred on nation-states. Are Jewish anarchists not Jewish because they don’t believe in any states? Was Henrietta Szold not Jewish because she believed there should be a single binational state in Palestine/Israel?
Language like “traitors” or implying that political support for Israel defines if someone is Jewish takes the complex nature of Jewish ID (which resists western Christian categories of religion/ethnicity/race/culture) & turns it into ethnonationalist political quasi-citizenship.
(It’s also worth noting that whatever else non-Zionist Jews might think of Eve, nobody is suggesting that she isn’t Jewish. None of us claim that Jared Kushner & Stephen Miller aren’t Jewish, as awful & heinous & racist as they are. Jews are not a monolith.)
Final thought: calling leftist or non-Zionist Jews “traitors” to the Jews & “not Jews” signals to right-wing Evangelical Christian philosemitic Zionists that leftist Jews are acceptable targets & that antisemitism vs. us isn’t “really” antisemitic since we aren’t “really” Jews.
It gives permission to right-wing Christians to attack lefty Jews “in defence of Israel” & thus justify all kinds of traditional antisemitism. It’s the logic that led Trump to claim that the 79% of US Jews who voted for Democrats in 2018 were “very disloyal” to the Jewish people.
(if you think this won’t happen to you because you’re a liberal Zionist, the right don’t distinguish between actual anti-Zionist Jews & liberal Zionists who are vocally opposed to the Occupation. J Street will get you called anti-Israel self-hating fake Jews just as much as JVP)
...and, I suppose unsurprisingly, Barlow has shared a tweet that misrepresents criticism (by Jews) of harmful or prejudiced things that she & others have written as an “attack” against those “who work tirelessly to counter anti-Jewish racism” ...
...and then goes on to insinuate that their Jewish critics are either recent converts or assimilated secular Jews who only recently embraced their Jewishness, implying that this would render their opinions less legitimate than her own.
