This week at the Edinburgh Festival Theatre – as he had at the city's Playhouse during the International Festival – choreographer Ohad Naharin arrived early enough for the show by the company he leads, Batsheva, to talk to those gathered outside.

In Scotland's capital, he has found – to a degree repeated nowhere else in the UK – that these will not be interested dance fans, but people who deem themselves to be political activists. Specifically they see themselves as pro-Palestinian, although that is the sort of misuse of language we also see in anti-abortionists describing themselves as pro-life. More accurately, the protesters are anti-Israeli and they gather to protest at the presence in the capital of the Tel Aviv-based company, which, they say, is funded by the Israeli state and is being used as an arm of its international diplomacy.

Much of this is debatable or treats half-truths as proven fact. Much like our own Scottish Ballet and Scottish Dance Theatre, the dancers are an international troupe and that is as true of the young company, Batsheva Ensemble, which was in Edinburgh this past week with Deca Dance, as it was of the senior dancers, who performed Hora in August. If the company, founded by American doyenne of choreography Martha Graham in 1964, are propagandists, they are peculiar ones: Hora included the music of the controversially anti-semitic Wagner, and parts of Deca Dance have, as Mary Brennan noted in her review in Thursday's paper, Arabic music in the soundscore.

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Perhaps Naharin was able to say some of this to the protesters outside calling for a cultural boycott of all things Israeli. That would have been a reasonable exchange of views in a democratic country. There is not, however, a cultural boycott of Israel in place and the extent of popular support for such a move is difficult to assess, although my suspicion is that it is nowhere near the top of the agenda of many Scots. Where it would leave those doing work across the divide – like Daniel Barenboim in music or the late Juliano Mer-Khamis in theatre – is a question that those who care about peace may be inclined to ask.

The Edinburgh protesters were not content to make their presence felt in the public realm outside the venues, however. During the EIF, and again this past week, they have purchased tickets for the performances and repeatedly interrupted them with their own less precise – but clearly synchronised – choreography of standing in their places in the auditorium, shouting slogans and unfurling flags and banners, until they were drowned out by audience applause and front-of-house staff ushered them out.

Whatever you think of the arguments on either side about the disputed lands of the Middle East – and, to be clear, I tend to believe that the continuing conflict is one of the many mistakes of the "settlement" after the Second World War, but that's where we are – this has been an extraordinarily misguided, not to say downright dumb, form of protest. It is patronising in the extreme to suggest that knowledgable dance-lovers need to be informed about the origins of the company and the political situation in that part of the world, and fantastically naive to imagine that anyone who has gone to see the show is likely to be persuaded to your cause if you interrupt their evening to shout about it. So even those inside inclined to be sympathetic to the rights of the Palestinian people to their homeland will have wanted to distance themselves from the attention-seeking wretches doing the shouting.

The broader constituency of support for the Palestinian cause outside of the auditorium might also be inclined to question the use to which their financial contributions are being put. By my reckoning, during the Festival and before this week's shows, the protesters spent what was easily a four-figure sum on tickets for performances they were not interested in watching – and I very much doubt those tickets were purchased with the personal cash of those occupying the seats. The boost to box-office receipts was one the EIF would presumably happily have foregone.

And what a hollow victory it will be if, despite the dignity with which the dancers comported themselves during the interruptions and the willingness of Naharin to debate, Dance Consortium decides that touring to Edinburgh for their companies to be abused is a fool's errand and leaves Scotland off its itinerary in future. Wha's like us, indeed?