This blew up pretty badly for me on one job. Among the people who would be materially responsible for a decision, there was unanimous agreement on which solution was right for the job. There were pretty senior folk. Half of them were the people you go to when you can't get anything to work.
The majority of the team did not agree with them. So the people who had no skin in the game were getting to set the agenda. Pretty big morale drop in that subgroup. I left while they were still trying to sort this problem out, but the feeling was somewhere between insubordination and strike, if we couldn't get the rules of engagement adjusted to weigh the opinions of directly affected individuals more highly.