something用于肯定句，anything用于否定句，所以我们说：

They are not doing anything extraordinary.

They are doing something extraordinary.

如果他们正在做不同寻常的事情，但自己却没有意识到这一点，我们用主从复合句，主句为否定句，但从句却是肯定句：

They are not aware that they are doing something extraordinary.

如果他们没有做不同寻常的事情，他们也意识到这一点，我们用主从复合句，主句为肯定句，从句为否定句：

They are aware that they are not doing anything extraordinary.

类似的例子还有：

He doesn't know he has made some mistakes.

He knows he hasn't made any mistakes.

本句中，主句They disregard social conventions 暗示他们正在某些不符合social conventions的事情，所以that从句应该是肯定句。我认为，本句中的anything不但可以改为something，而且改用something更符合整个句子的语境。

that从句用肯定词还是非肯定词，不是取决于they是否意识到他们做还是没做某事，而是取决于说话人认为他们做了还是未做某事。而句首的they disregard soical conrentions 强烈暗示他们正在做某事，只是他们没有意识到而已。that从句是个肯定句，应该用肯定词something, 而不是非肯定词anything。