Definitely the overreacting organised group, but also a large amount of blame falls on the media helping them promote their overreactions to the masses
You really need the media to have a moral panic, because without them you can't get the feedback loop going. I deliberately draw analogy to the audio phenomenon here. No matter how much I scream and yell, even in front of a crowd of people, I can't create a feedback loop without a microphone.
The reason why the moral panics in the last couple of years have not been from the religious right isn't so much because they've particularly changed, but because the media isn't willing to push those anymore, and the media on the right just isn't large enough right now to sustain their own. (Give it another three or four years at current pace, though.)
Definitely the overreacting organised group, but also a large amount of blame falls on the media helping them promote their overreactions to the masses