Definitely not the most hated club. Just imagine how much more virulent it would be if Liverpool, Man U or Chelsea were struggling. The motive is broadly the same just that in the case of Newcastle there is currently the opportunity as well. As others have said, if we (Spurs) were in the same position the general feeling would be the same, maybe worse with an anti-London/southern media mafia slant tacked on.
I think you can look at any inter-club hatred coming from various angles - 1) local rivalry 2) tall poppy syndrome 3) rivalry between peers 4) personal resentments/jealousies. At the moment, Newcastle ticks a lot of the boxes. 1) Boro & Sunderland 2) smaller clubs 3) Man City/Spurs/Villa/Everton and I'd actually say some residual Big 4 rivalry (it wasn't that long ago) 4) any club with smaller attendances, less media spotlight, smaller wage bill - or who've got mates who are Newcastle fans and enjoy a bit of a laugh.
When I was growing up in N London in the 70s/80s I hated Arsenal (1, 2, 3 & 4) and Liverpool (1, 3, 4 - so many bloody glory-hunters). I only knew one Man U fan and Chelsea weren't a threat so I've never hated them.
It's schadenfreude. Most fans have the same delusions just some teams can live up to them more often than others.