Is the Nightmare verse like the third reich? But instead of Jews Nightmare moon kills earthponies because they are not as useful for war like pegasi and unicorns?

Not unless she honestly considers "the reason everyone doesn't starve to death" to be useless in war. Ponies end to respect other ponies and look down on other species. At worst, earth ponies would be a lower rank, but honestly producing rations (especially in a world without a sun) sounds like one of the most important jobs someone could have, if you ask me.

6979864
So why ponies hate her? To me she's like celestia, there is no different way of ruling there

6979853
Careful now. That’s a very sensitive comparison to draw, and I won’t hesitate to lock this if I need to.

However, I don’t recall seeing anything in S5E26 to support that Nightmare Moon hates earth ponies. 6979864 makes an excellent point about the importance of earth ponies in a world without the sun to help with food production. Even if NMM isn’t fond of them for some reason, she probably needs them.

As for why ponies might not like NMM: consider that there are already all kinds of reasons why people don’t like leaders who can’t control the day and night. But in NMM’s case, it seems like she doesn’t let the sun shine at all. Plenty of ponies might have problems with that.

6979954
I know it's a sensitive thing, my grandparents suffered in the holocaust, and I'm sorry if you thought I meant to compare Nightmare moon to nazis. I just had an idea for a story, but I do not understand the idea of the different between the nightmareverse to the normal verse.

6979956
I am sorry about your grandparents’ suffering, and any effects on your family.

For what it’s worth, I don’t think there are a lot of canon rules about what the Nightmareverse has to be like and how it has to be different from the main universe. The main things we know for sure are that NMM rules Equestria from a restored Castle of the Two Sisters, Celestia has been banished to the moon, and Rarity & Rainbow Dash work for NMM. You’re totally free to explore things beyond that.

In my own Nightmareverse story, I dabbled in some worldbuilding about food production (and shortages), as well as what happened to several other canon characters like Twilight and Starlight. I gave NMM a hatred of pegasi, and made it so that she wanted to either convert them to thestrals or kill them for their “impurity.” And I included a Resistance led by loyalists to Celestia, who kept up the “good fight” from their hiding places.

But those are just a couple of ideas—there’s lots of room to play with it.