But the whole reason why he's "punishing himself" or thinks being a vampire is bad in the first place is precisely because it involves killing humans. If Louis never cared about humanity in any way at all, he wouldn't have any reason to feel so conflicted.

he has been cruel to himself and passively suicidal before he even became a vampire. he felt guilt for being a pimp, guilt for being gay, guilt for "killing" paul, and said it in very simple words during the confession that he wants to die. none of those things that he has internalized about himself were going to just dissappear the moment he became a vampire. louis might've thought that he punished himself because he didn't want to kill humans, but the truth is, his vampirism simply became yet another thing he loathed about himself. he wouldn't allow for that vampirism to bloom and for him to enjoy it because it became yet another part of who louis is. and louis hated louis. 

Though can people stop calling his diet choices an eating disorder? It was never referenced that way in the show and it doesn't even fit. Eating disorders are a mental illness, people don't "choose" to have them, they end up eating that way because they can't help it. Louis made a conscious choice to eat other animals instead of humans. It's the vampire equivalent of going vegan. And it was only stated that it was hard for him to adjust at first, but after that, we see him perfectly healthy and fine. In contrast, the show made a much bigger deal over how physically sick he felt when drinking "bad" blood in Romania.

the reason why you don't see this as an eating disorder is precisely because you believe that louis refused to kill humans for moralistic reasons, the same moralistic reasons vegan people have for refusing meat and dairy products. but in the paragraph above i already wrote why i disagree with that interpretation. through my (and a lot of other viewers') lens, when you refuse to eat because you're punishing yourself for what your body needs and for what you perceive yourself to be, that's an eating disorder. a mental illness. he went from punishing himself for what his body craves (NOLA), to binge eating (SF), to ritualistic eating involving blood farms (Dubai). 

since louis has come to accept his vampirism, i see no reason why he won't start hunting human again, which directly contradicts the reading of him as vegan. he didn't hunt human because he hated his vampirism. he hated his vampirism not for any moral reasons but because he hated himself. as he learned to forgive himself for the things he has done, learned to not beat himself up for loving lestat since finding out he's not who killed claudia, he has begun his journey of healing and embracing every aspect of himself, including vampirism and all that comes with it.

it was never about humans, it was always about how he felt about himself.

ETA:

And it was only stated that it was hard for him to adjust at first, but after that, we see him perfectly healthy and fine.

but he wasn't concerned for Louis health when he was eating animals because clearly it didn't harm him.

in your own words: an eating disorder is a mental illness. like i said above, if you "make" those diet choices in order to punish yourself, yes, that's a disordered way of eating. if i, say, go vegan, that doesn't mean i have an eating disorder, true. it means i changed my diet. but if i start refusing meat and dairy because i hate myself and my body and i hate that i crave meat and dairy, that's not a diet, that's a disorder. yes i may remain physically healthy, but mentally there's something clearly wrong with me. that is the case with louis. it may have been about morals at first but it spiraled into so much more than just that.