Sorry, too long of an OP to read right now (at uni, so mixing typing and listening... ^^). My quick 2 cents though are - mostly the groups don't hate each other per se (there are always idiots thinking they're superior on the usual bullshit grounds of "my epeen's bigger than yours" and "you don't have a life", but I don't find those serious arguments and thus worth considering). What they hate are two things:
1) Playing with each other - these two groups have two different goals. Putting them together just doesn't work. I've been playing WoW for a LONG ass time before so I've had a chance to see it from both sides. From the casual side, I can tell you I hated some of my first runs through 5 man dungeons with hardcore players. They were rushing through the instance and I didn't get to take much of the instance in or get much fun out of it because I was struggling the whole time to just keep up with them. In the same way, after a long time of playing hardcore, I know it's a pain in the ass sometimes to have someone who's new cause they're just seemingly slacking behind.
Another, more to the point example, being in a mixed casual/hardcore guild was a fucking nightmare. Casuals play for chilling, so they wanna chill out in an easy instance. Hardcores play for the challenge, so they wanna get some progress done. I have to state here, BOTH groups play for FUN - they just have a different definition of what fun is for them. Anyway, you go to an easy place, hardcores are bored. You go to a hard place, the casuals are struggling and hardcores feel like they're being held back.
Outside each other however, these two groups can love each other. I've been in and seen some VERY successful mixed guilds. Everyone chatted together, even played together a lot, but the main stuff they were there for (raiding) was split, you had casual raids and hardcore raids. I've also seen and again, been in certain hardcore guilds that had sister casual guilds. I've also seen great relations between random hardcore and casual guilds. All that can work, just don't force them to work together on a goal they don't agree on. There is NOTHING unusual about not wanting to play the game for someone else, team work is one thing, spending your free time doing something you don't enjoy is completely another.
2) Effect on the game - This is where most of the public hate comes from. Fact is, designers don't make two games. They make one game both hardcore and casual players have to play. So when they make something that's more suited for casuals, the hardcores are not happy. Likewise, when they make something that's more suited for hardcores, the casuals aren't happy. Both groups complain, either about the game being changed to be more casual or more hardcore.
Again, the complaint is not unreasonable. Everyone wants the game experience designed, not for them, but for something they can enjoy and a perfect balance in hard to get right. Both groups are sort of "logically and rightfully" pissed off at each other, because if the other one wasn't there, the game design would shift accordingly towards what they're looking for. That's not to excuse outright hate for people just because of how they want to play the game however - everyone deserves an enjoyable experience. But towards the game designers, it's a very valid complaint and something they constantly need to work on and some friction between the groups is not at all unusual over it because they're both asking at the same time for two different things.