A commenter named Ram left a brilliant comment over at TheMoneyIllusion. Here it is (emphasis added):
I'd contend that the main problem in America is that the public, including its highly educated members, is social-scientifically ignorant. Most people I talk to about policy do not even realize that there is anything non-trivial about policy analysis. They want the government to make sure that four phases of rigorously designed RCTs be performed before drugs are made available to the public, for fear of unintended consequences of intervening on a complex system like the human body, yet they think they understand the consequences of highly complex interventions on human societies by introspection alone. Not only do they think they understand the consequences of alternative policy choices, but they're so confident that their understanding is right and that its truth is so obvious that the only explanation for disagreement is evil intentions. When I point out that on virtually every policy issue, at least somewhat compelling arguments for many conflicting points of view have been made by relevant experts, people usually react in disbelief or denial, or immediately retreat to questioning the motives of these experts ("of course they say that, they're on the payroll of Big Business" or whatever). These patterns of speech and behavior are uniformly distributed across the political spectrum, even if intelligence and knowledge of well-established facts is not. Even many experts in particular areas of social science evince no awareness of the lack of expert consensus on almost anything in their field, and give the impression of unanimity to an unknowing public.
My guess is that if you were to convince a supposedly non-utilitarian person that their (e.g.) deontological prescriptions might have terrible consequences, then they would revisit them. Anti-consequentialism is easy to maintain so long as you believe the consequences of your proposals are desirable, but most would fold if convinced otherwise. The real problem is convincing anyone, which involves first convincing them they don't already know the answers, which involves getting them to disassociate with their political allies enough to think critically, which involves upending a defining feature of their identity.
Imagine how different the world would look if, in order to secure the most votes, politicians had to say "you know, I don't really know the best way to deal with this problem. My educated guess, based on consultations with experts, is that we should try X, but the truth is no one knows if it will be a change for the better. Consequently we will undertake a small scale experiment, designed to maximize our understanding of the consequence of X. Should it succeed we will scale up and perform follow up studies. Should it fail we will scale it back." Seems to me we will never get there till the public becomes cognizant of and concerned about its own policy ignorance. The details of moral philosophy will be easy to reason over once we've managed that much.