Happy I wondered whether the play might transfer to the Royal Court on the basis of its now undeniable 'edginess' - but I think it's unlikely.
UnisS there are masses of rubbish, under-rehearsed plays that still go before paying audiences. NYT tends not to produce them, but anyway, whilst NYT's standards are generally very impressive, its productions - and particularly a play like this - have a wider purpose than just being slickly produced.
almondcakes - young people in east London are seen to be particularly at risk of radicalisation - and with good reason. There's every reason why these young people should be able to explore and express these issues and their experiences. (OMG I sound like a preachy community theatre practitioner, but hey ho.) It's possible, likely even, that young people from groups like those that you describe have contributed to the play.
Farahilda - interesting, but unlikely.
I think that it's simply that there are fears that there would be violent responses to the play, and it's easier to scrap it than to try and ensure a safe environment for it to take place.