One possible take on this statement is that it was a cautionary statement.
By writing down “If you read, you will judge” he was mentally protecting his writings. It provides a disclaimer of sorts. Any opinion you express on the writings are your own judgment, therefore he could feel free to write whatever he wanted. If you had a problem with what you read, then he could easily rely on the disclaimer (at least internally) to discount your opinion as judgment of him – something which you would have no valid claim to do.
Anyone who has ever tried to start a journal will know that it can be difficult at first to put your thoughts down openly – someone else might see them! And if they read them it will be from their own perspective – not yours, and they will potentially pass judgement on your thoughts and feelings. It’s enough to cause some to drop the task out of frustration. Out of fear they can only be superficial in their journals and the positives of writing are lost.
Perhaps this statement was Cobain’s way of overcoming that fear of personal judgement.