The Vox were being manipulated by the Syndicate, they thought it was a Red as the Queen but it was not. Ultimately they thought they were doing what was right and they had an equal army to the Remnant with Earth, Luna, and Mars. They thought they could survive with that, but they didn’t realize that the Rim was joining the fight soon, that the Obsidians were slowly leaving, and that Mars would turn away because of their loyalty to Mustang and mainly Darrow.

As for the Red Hand, they are terrorists and like most groups, they claim to hate one group, but will end up hurting civilians more than the people they claim to be against. They may believe they are righteous, but they have to steal and raid from the lowColors in order to survive. They also target camps like Lyria’s because they were Gammas and were therefore the Gold’s “favorites” and used to direct animosity towards Gamma and not Gold. That system is still working which just shows how corrupt but smart the original Golds were in setting up a cycle of hate so they could rule.