She hasn't yet filled the post or filed a single line of copy, but the incoming New York Times correspondent for Jerusalem has already been judged. And it's damning. Apparently, soon-to-be bureau chief Jodi Rudoren has been sending bad tweets to the wrong people and that's enough to have Israel's rightwing defenders denounce the journalist, within hours, as biased and "anti-Zionist".

She should not be tweeting "cutesy missives" to Electronic Intifada co-founder Ali Abunimah. She shouldn't be approving a forthcoming book titled The Crisis of Zionism by American writer Peter Beinart. In fact, the most benign critics suggest, she should not be tweeting at all – which, we can guess, would not be the case had she decided to post about, say, the dry weather and deluge of hummus that await her in Jerusalem.

You could just dismiss such hasty and ill-founded pronouncements as idiotic. But the New York Times thinks it all significant enough actually to have responded to the complaints, assuring that the paper has "complete confidence in Jodi's fairness and integrity as a journalist" – adding, with an obviousness that must be spiked with sarcasm: "If we didn't, she wouldn't be taking on this assignment."

The incident is part of a broader rash of pouncing-upon from rightwing pro-Israelis that has sucked the oxygen out of any conversation about the country – especially in the US. Witness the recent storm over the phrase "Israel firsters": used to accuse people of putting policy on Israel above US interests, it sparked a row among liberal commentators on whether it carries connotations of dual loyalty that feed into antisemitic tropes. This was just another attempt to smear liberal American critics of Israel, and fed into the frustration over such blockading – best expressed in the title of one recent post: "Dear Israel lobby, we give up – please give us an acceptable way of insulting you."

Yet the real danger in all this is that the rush to throw charges of antisemitism at people who criticise Israel will desensitise vigilance over the real thing. Such tactics are meant to intimidate and paralyse, choke and divert the discussion over Israel's occupation and policies in the Middle East. But for every person silenced, there are growing numbers who, surveying the quality of the argument, will dismiss the pro-right Israel lobby solely on the basis of the bullying. It isn't just the nature of the bashing, but its compulsive frequency, especially when set against the paucity of actual arguments presented.

As more commentators are now saying: the trouble with this rightist campaign over Israel is in the content, which always trumps the delivery system. Incidentally, this is the theme of one of the articles that Rudoren was lambasted for tweeting, which quotes Beinart, from the book she wasn't supposed to like: "Israel does not have a public relations problem; it has a policy problem."

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• The headline and subheading on this article were amended on 17 April 2012. The originals incorrectly implied that the New York Times's new Jerusalem correspondent had been accused of antisemitism