Keep in mind that it may not have been the entire Brotherhood that fought the NCR. The Mojave chapter is but one chapter, and may have been considered rouge by the Brotherhood at some point given that Elijah was kind of batshit insane and did insane shit and that it's quite likely there's been no contact between the main Brotherhood and the Mojave Chapter since the incident at Helios. If I remember correctly there's supposed to be a state in the NCR called Maxson which was named for the BoS founder, and that the territory of Lost Hills was, despite it's proximity to Shady Sands, independent BoS territory. Hell, in the second game the Brotherhood was implied to be on pretty good terms with the NCR.
So yeah, wouldn't put it past the main Brotherhood council to declare the Mojave chapter rouge and tell the NCR it's fine to fight against them. Why the fuck would you risk war with the NCR over one batshit old man's vision which we find out is even fucking worse than Caesar's?
Edit: Something I completely forgot that adds some credibility to this theory: Christine Royce, after Elijah used his influence to fuck over her relationship with Veronica, ends up joining the Circle of Steel which is an organization within the Brotherhood that is basically their secret police. She was sent to actually execute Elijah for his betrayal of the Brotherhood and probably for jeopardizing their relationship with the NCR. And also because he's a dangerous and deranged old shit, as we see throughout both Old World Blues and Dead Money.
It could be seen that the "alliance" between the NCR and the Mojave chapter is less an actual alliance and more the Mojave chapter being brought back into compliance with the alliance already established between the main Brotherhood and the NCR.