I get Hellscream. It's not hard to, really.
Hellscream isn't hard to understand. His goals are clear, and are atleast somewhat justified.
But from entire cultures to a handful of individuals, it isn't surprising to see that his methods have ruffled the wrong feathers. It doesn't surprise me, or even strike me as something to be confused about, to see dissent. Some people have more a right to complain.
There's a lot of people that can hate him, especially because of his actions. I'm not surprised by it either, because Blizzard seems to want us to dislike him, and there will be dissent during the Siege of Orgrimmar. There already seems to be plenty of reason to go against him.
Some people have a better perspective on everything as well.
Some people have hated him OOC from the start and that shows in their characters.
After all, we can't go from "Hey he's a badass, right on" to "!@#$ YOU HELLSCREAM GIMME A CIGARETTE" in the span of the days before his swan song patch's release. Reasons to dislike him are being developed, some of which are more blatant than others.
There is a reason why he is being taken down, and the path to his down fall is kinda logical, because he is a badass, with good intentions, but, he's doing things the wrong way, which has been a build up. People have enough reasons now to hate him, and more are being made as the game goes along but I don't think there should be so many people that hate him right from the start.
I think the oddity comes more from location, though. That goes back to Guard Awareness Syndrome, and whether people are aware of what they're saying/doing and where, or not. Moreso, if they even care. Every city has its people that are like "hey I do as I please to hell with these guards."
It's where that dislike is shown at, that's the problem. You shouldn't show that dissent in front of guards in Orgrimmar, you can't even say you hate Garrosh, or make plans in the open to go against him, because brutal actions would be taken. This is important, because it contributes to the arguement that guards are just NPCs and should be disregarded in RP. Every race has it's subjects that shouldn't be openly mentioned in cities for being allied with, such as Grimtotem in Thunder Bluff, and Scarlet Crusaders in the Undercity.
That's an issue which prevails on either side of the fence. Garrosh Hate, or at least its openness, is just a prominent fallback.
The same can be side on Alliance side. Similiar reactions would be had if someone in Darnassus said they worked with Satyrs, people in Tinkertown saying they support Thermaplugg, or back in Vanilla people in Ironforge saying they supported the Dark Irons.