People with certain kinds of psychological disorders and conditions. Functional sociopaths, psychopaths, and narcissists tend to develop a morality along these lines. They create this form of morality as a construct to survive, Some of these are usually considered amoral, or lack of a recognition of morality; however there are people like this who hate things that are absolutely normal, accept things that most people disdain, and judge other people by things that are usually not associated with morality.
While not quite to the extreme of 'bacon and necktie', some high functioning Autistic people claim that things seem to be this way, whether they want to think like that or not. While neurotypical people think about a topic one way, the Autistic subject has an unwavering alternative view on it, which is often rebuked equally unwaveringly by neurotypical people. This can be a distressing problem and a source of considerable conflict and, eventually, depression. Imagine a world where everything is just wrong, but everything and everyone around you thinks that's not true.
Most animals don't even have concepts of morality or empathy. Those that do (apes, dolphins, dogs, etc.) tend to be absolutely incomprehensible to humans. For example dolphins will aid sick or injured creatures (even those not of their species) and have even been known to rescue humans from sharks, but the males are casual rapists (to the point that they'll sometimes beat baby dolphins to death to force the mother to mate) and some dolphins are sadists and brutally kill other animals for fun. How they reconcile such behavior is simply unknowable.
According to Kohlberg's theory of moral development, humans are this to each other. Humans progress through different value systems as they age, starting as infants and toddlers (as stated above) with a pure pleasure/pain dimension and eventually maturing toward more and more complex systems. Those at different stages really don't understand each other at all, especially when the less mature try to comprehend the more mature. However, Kohlberg was famously criticized by feminist philosopher Gilligan, who claimed his theory was androcentric and focused entirely on the concept of morality-as-justice, while women cared more about morality-as-care. Other critics question the entire idea that morality is governed by principles such as "justice" or "fairness," and believe humans really have an evolved emotional repertoire which is based on our emotions and developed for other reasons. More at the Other Wiki.
Similarly, Stephen Pinker assembles other works that come to define systems for moral thought used by humans, namely Communal Sharing (including in-group loyalty and purity/sanctity), Authority Ranking (obey your superiors), Equity Matching (sharing), and Rational/Legal (markets and laws). Each of these has a different neural pathway in the brain and each normal human uses all of these. No system is strictly better or worse. Each has its moments in different situations. He then establishes that a person understands a moral issue by applying one or more of these systems. Anyone who uses different models than you then becomes Blue-and-Orange to you. For example, a restaurant is governed by Rational/Legal morality. No one goes in and after the meal offers to repay the chef by hosting his or her family in the future (Equity Matching). Applied to real dilemmas, consider same-sex marriages. Conservatives view it through the purity/sanctity aspect of Communal Sharing and Authority Ranking with religious authority as the authority figure, while Liberals tend toward a Rational/Legal point of view. The two sides literally do not use the same brain system to examine the issue.
An important point is that all of the systems are valid at times and anyone using a different system will seem to just "not get it" in a blue-and-orange way. Imagine paying for a parking spot on a busy street when a cop comes and orders you to move your car because an ambulance needs access where you parked. Most of us bow to Authority Ranking and believe moving our car is the right thing to do. Someone who engaged in Equity Matching by asking the officer if he could park in front of the cop's house sometime or stopped to argue with the cop about the legality of forcing you to move and when you'll be compensated for the cost of parking (Rational/Legal) seems blue-and-orange to us.
Source, especially from the chapter "The varieties of Moral Experience" onwards.
Similarly to Pinker's assessment is Jonathan Haidt's observations, which became the basis of The Righteous Mind. In essence, there are moral foundations that can be classified under broad categories like care, fairness, liberty, loyalty, authority and sanctity. He asserts that not only do these impact one's individual moral framework, but that these can also lead to wildly differing views, beliefs, ideologies, etc. based on what foundations take precedence. As a consequence, this can help explain why Right and Left-leaning people can view the same thing in incredibly varied interpretations and why it's difficult for human beings to talk on the same page.
Idealism and Cynicism. A living, breathing meta-example of the human psyche that becomes the third scale of morality. Usually, it tells whether such an individual is either determined to act or preserved in such a way that they cannot act yet still possess the morals of the other two dimensional morals.
Some schools of philosophy can come off as this to non-adherents, as they are able to take normative and existential stances that are entirely invalid or even evil when compared to the listener's. Take, for example, the Mohists, who promoted a sometimes fairly modern-ish consequentialist line of thought...viewed entirely through the lens of what is best for a unified authoritarian state, and has been noted as not all that dissimilar to what Ingsoc is supposed to be.
Most ancient Bronze Age, Iron Age and Classical Pagan religions and societies would appear to modern day human as such. For example, it was considered perfectly legal for the creditor to sell a bankrupted debtor to Gladiator Games, where he could well get killed or maimed.
Perfect rationality in game theory can often involve so many logical twists and turns that it appears incomprehensible rather than merely selfish. For instance, in the pirate game, pirate A's motivations are pretty clear if he tries to keep 98 out of 100 coins for himself. But would pirates C and E really be happy with only 1 coin each?