I mean, dude, it's the military not a cruise ship.
From what we have seen the food, while not 5 stars, isn't awfull and the crew seems to have relative much freedom, neither seems the captain overly harsh/tyranical. The MC's comment should be taken with a grain of salt, as he comes of as a rather immature show-off, which was a civilian just before.
A captain isn't supposed to be best buddies with the crew, a professional distance is normal and expected in the military.
Also she didn't rat out anyone, she followed the law, as is expected from her position. IIRC the law sees ai experiments as high treason, so not something small which you can look away. That the experiment turned out good and helped does not change the fact that the mechanic broke the law, way before that and fully aware what she did is a crime, and not a small one.
You will have the same situation with our laws today, even if you do the right thing and help someone, that doesn't prevent you from being punished for a comited crime.
Also punishment for mutiny is usually very harsh, one of the most serious crimes in the military, with life imprisonment or even a death sentence in serve cases.
Nothing we have seen so far would justify a mutiny, not even close...frankly, most of my superiors in military were harsher than our good captain.
And not liking the captain, or how she leads, is in no way a justification for a mutiny.