A mutiny is a mutiny, justified or not. And stranded on an alien ship you barely control dependent on technology you scarcely understand is about the worst possible circumstances to attempt a mutiny unless you are absolutely sure you have no other choice.
It might have been different if the series had spent more time portraying Rush as something other than self-important dooshbag (or if Young was stranding/executing people at random). Otherwise the entire "revolution for democracy!" angle came off as more of a clique war between the civilians and the soldiers, with the former faction having its priorities thoroughly ass backwards and the latter faction having no coherent priorities of any kind.
Young had been lurching the crew from one disaster to another, almost entirely down to the fact that he wouldn't listen to Rush, worse than that, he actually tried to murder the man, the one expert the crew had and despite his ulterior motives - the man they depended on most. They were in an extremely hostile environment, their lives in jeopardy on an almost daily basis, all the while being lead by an inept commander who had appointed himself dictator. A man that was in large part responsible for their constant state of peril. From their perspective, removing him could be the difference between life and death. Of course
they were going to do something, especially after talking had failed and especially after Wray found out what he'd done to Rush.