I think it might be a weird plothole, her infatuation with Naruto went too far compared to how much she believed in him. If you know he never gives up you don't panic just because he fights a classmate..
I think it's also made to contrast Sakura's love for Naruto and highlight that it's more healthy than Hinata's. In the two scenes I was talking about, they react to Naruto's actions in opposite ways, just panels from eachother.
I'll agree with that, part 1 plays this beautifully showing that the one who truly believes in Naruto is Sakura. In fact I said as much in on of the other replies to you.
Honestly though it's a garbage plothole, there's still no reason for Hinata to even crush on Naruto. I hate SS even in Part 1 though I used to ship it, but it makes a bit more sense in part 1. Sakura likes Sasgay bc he has it all. The looks, the dark backstory, the skillz, etc. Not enough for love mind you but still lust and crush. But SS should have died after Part 1. Not remotely enough there to convince anyone that they actually loved each other.
When one looks at things, Hinata really doesn't like "Naruto", she likes her mentally idealized version of Naruto.
Just like how Sakura and other fangirls only liked their own mentally idealized version of Sasuke, "the last Uchiha" (some sort of dark, mysterious prince on a white horse who will come to their rescue, sweep them off their feet, and other fairy tale fantasies), but not liking, or even knowing, Sasuke the actual person.
However, whereas Sakura, at least initially, was moving on from Sasuke because she was made painfully aware that Sasuke the person was nothing like how she thought he was in her fantasy crush, Hinata never, ever moved on from that crush on her mentally idealized version of Naruto. Even as an "adult", she only sees that version of him despite Naruto himself proving he's not like that.
Agreed, but the manga says it was "true love"
The problem is once again why does Hinata even like Naruto in the beginning? Here's an easy fix, HAVE HER FALL IN LIKE WITH HIM AFTER HE DEFEATS NEJI. Then the whole It's my nindo too sounds a bit less cringey.
I think Sakura crushing on Sasgay is fine in part 1. I wouldn't even mind it if he reciprocated a bit and there was a serious romance there for a bit of flavoring. Both make sense and help set up Sasgay's Face heel turn better emphasizing how he is giving up everything for revenge. Then it makes more sense for Sakura to "love" him later on.
It's just really obvious that there was a civil war in SJ over Naruto pairings, one chapter Sakura hates the Sausage and crushes on Naruto, another Chapter Naruto is holding Hinata's hand, then she is tripping on a rock.
Just so much wasted potential
When you think about it, Hinata's crush really doesn't have a solid basis to it at all. Admiring a person for their determination and seeing them as a sort of role model is one thing, but a crush? If Hinata liked Naruto for other reasons like his kindness, goofiness, etc, then there would be more meat to it. But honestly, it would've made just as much sense for her to fall for Rock Lee if iron-clad determination is all it takes to make her fall in love with someone.
That's why I say if you really want to go the NH route have her ignore him at first then fall for him after he defeats Neji in part 1. It gives a reasonable explanation for the Nindo admiration thing and adds a personal touch to what should be the beginning of the romance. Let me take a trip down memory lane and give an example:

This is an excellent example of how to start a romance. The connection is cemented when Naruto points out that he likes Sakura bc they both want acknowledgement. The personal emotional touch is there bc we sympathize with his kindness as he says he loves her forehead which she hates. And to top it off, later on Sakura comes to appreciate him a bit more after getting called out by Sausage.
That's what NH lacks, and why it's so popular. No effort needed, as long as you say you'll never give up you win the kittens. In other words talk kitten even if you can't back it up and you win. Weeaboos love that crap.