It is called propaganda and it exists on both sides.

As soon as the war broke out and there were problems with internet connectivity to Israel according to netblocks.org there was a huge drop in anti-Christian/Christianity is Jewish threads, India hate threads, lolicon threads, and furry threads on 4chan. I have seen many attribute these provocations to JIDF in the past. There is a full time Israeli team dedicated to messing with people online. I have no idea who actually bankrolls these guys or if they are volunteers.