Remember that Sera is not Earth. On Sera, humans are said to be “more evolved” and have less body hair. That’s because Epic didn’t want to put armpit hair on the Gears 3 characters.
Sera is simplified, and in some ways idealized. Cliff and Rod stated after Gears 1 that they set out to create a “United Nations cast of diverse characters and ethnicities.” Real life socio-political issues took a backseat, because the games don’t focus on that. They leave it in the background to remind players “you’re not fighting for good, you’re fighting for the lesser evil.”
The Old COG had the birthing creches. Women were paid in extra food and security to become breeders, and as if that wasn’t dark enough, some of the birthing creches broke the rules. The COG eventually lost them all, or disbanded them all, and nixed the idea completely when the COG dissolved. That was the one and only civil rights issue that was directly addressed by Gears. And they only addressed it in the comics, because the birthing creches were mostly gone by 14 A.E.D.
The New COG focuses more on social engineering. Men and women are back to being full equals, as they were during the Pendulum Wars. The only divisions are biological. Women have always been allowed to serve in the COG and the UIR militaries. We didn’t see women politicians in the Old COG, but a woman leads the New COG (and she’s just as slimy as Prescott).
We’ve seen how Outsiders resist the New COG, and many of those Outsiders were quite eloquent. Well-informed, even. Some weren’t. Others didn’t care. None of that matters now, because all the Outsiders are dead, or they’ve joined the COG’s military. The COG is once again the lesser of two evils… And the Swarm is more evil.
So what’s Kait supposed to stand against and oppose? The Swarm, and Jinn’s authoritarianism. She already opposes both.
Kait calls her own shots, listens to the advice and orders of those she considers wise, and she verbally dominated Jinn in Gears 5. What more can she do? Seize control of the COG and change the government’s diapers? No. If she survives the Swarm war, Kait will pull a Reyna (EDIT: and a Gabe) and found a new civilization. Until then, Kait’s already stepping up and taking responsibility.