How many times have you seen people disqualify logic for the sake of morality?

People say they try to be logical and do logical things; for the opposite would be illogical or insane. Not that some would know it, but they unwittingly derail logic for the sake of morality. Logic has no foot in morality. For instance, a chain is supposedly as strong as its weakest link. As a distressed or impoverished community, society, etc. if you can remove the weakest links, overall it would be better for everyone, especially if it came to survival or battle. Some, maybe many, would try to override that logic with morality because no one wants to seem heartless and admit eliminating the weak, old, and cripple would be the best move to maximize the available resources for those who can actively support the community fairly equal to everyone else and to what they will consume in resources. There are many other examples of logic appearing immoral and thus people don’t want to embrace it. Have you seem instances where logic in not applied because it would go against some standard of morality a community has set in place?