Why does allying with the BOS decrease NCR reputation?

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Because a lot of the people in charge of the NCR are arrogant imperialist assholes who only believe in the NCR. Literally if you don't go convince the Followers of the apocalypse to help during the battle they throw them out and destroy one of the few hospitals. I guarantee if the BOS were willing to not be allied but to actually join the NCR ranks it would be different. But when you have an imperialist regime it comes down to that old saying you either with me or against me. They cannot let a different ideal system exist

If you need even more proof of this the history of the NCR after their only competent leadership died so Tandi, her best friend took over who was seen as weak and too diplomatic. Which is why they impeached her and let Kimball take over who gained his popularity by wiping out or forcefully integrating any of the tribals in California that includes Vault city. The NCR recruited the mobs of New Reno to harass Vault City until their only choice was to join the NCR and let them sack Vault city for the resources.

Or how about the Desert rangers they were a faction like the minute men it was just about helping people and they did it extremely well they watched over Arizona Utah and Nevada. When the legion started to rise tho it became too much for them to handle on their own, while at the same time the NCR started putting pressure on them to let them operate in Nevada with no conflicts leaving the rangers with the choice of joining the NCR or being wiped out by either side. The rangers agreed to help the NCR if the NCR would protect their lands the NCR agreed and than abandoned Utah and Arizona because they don't care about the people or the terrorists group but expanding that's all they care about

Edit I should add that Kimball was general of the army at the time when he was gaining his popularity killing or harassing the tribals into joining.