Some definitely do want Naruto to hate Sakura, based on the anti-NS/anti-Sakura fan art I've seen. However, some NH fans want Naruto and Hinata to get together, but they also want Naruto and Sakura to stay good friends, which is a mentality that I'm very fine with even though I don't exactly agree with it.
It will vary depending on the fan - just as it is with any portion of the fandom. There are extremes in every Big 3 pairing fandom to be sure.
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Yep, many do think it would be horrible to do that. Some NH fans also feel that Naruto, because of his past, will easily fall in love with Hinata after learning that she always liked him. Some even say that Hinata has always been there for him, which doesn't seem to be true from what we've seen.
To be honest, I think Hinata would have a much, much better chance of winning over Naruto if she had befriended him as kids, or if she had confessed much earlier. If in chapter 3, Naruto had introduced Sakura as his crush, but Hinata as a close female friend who has always been there for him, then NH would have much greater stakes in my opinion. In the anime, Hinata appeared in episode 1 just like all of Konoha 12, but in the manga, she only appeared in chapter 34.
I completely agree - I think this is best shown in Naruto's mentality during the Gaara fight. That fight occurred after all of his development with Hinata in part one (and the majority of his development with her overall, given there was so little development if any in part 2), and yet she was not in his thoughts at all as one of the people who were so important to him. Those spots were reserved for Team 7 and Iruka, because they were the first ones to acknowledge him. They saved him from the hell of loneliness, and for that, they will always hold a special place in his heart that no one else can replace.
I think that if Hinata were going to be important to Naruto, enough to get together with her, he would have at least thought passingly about her there - but he didn't. He didn't think of her at all after the Neji fight was over and done until he met up with her again in part 2 after the Rescue Gaara mission.
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I don't hold anything against Hinata for not helping Naruto though, because at least she liked Naruto instead of hating him and Hinata being the first person to befriend Naruto would have ruined the impact Iruka had on Naruto.
My only problem with Hinata not helping Naruto before the chuunin exams is the fans who will argue vehemently that she's always been there for Naruto, and that she was the first to recognize him for what he was - to me, that's practically meaningless because Naruto was completely unaware of it. She might as well have given him the cold shoulder like everyone else at that age for all the difference it actually made to Naruto.