Currently the US is caught between two distinct moral universes:
One moral universe (mainly associated with conservatism) is roughly Kohlberg stage 4:
- Authority and social order are both paramount and intrinsically good; disobedience is intrinsically bad
- Uniformity and equality are presumed, and any suggestions of systematic or structural difference is rejected out of hand because it implies that authority and social order are not intrinsically good
- Most problematic (criminal) behavior is consequently viewed as the actions of lone individuals; such individuals are seen as morally weak or as lacking moral standing entirely (like animals)
Police hold a particular problematic standing in this worldview. As guardians of authority and social order they are perceived as intrinsically good, and almost any behavior they engage in can and will be explained away as necessary to preserve the intrinsic good of authority and social order. Further, any officer who oversteps even this leniency will invariably be cast as a lone individual working against the law and social order.
The other moral universe (mainly associated with Left-liberalism) is roughly Kohlberg stage 5:
- Law and social order are part of the social contract meant to guarantee everyone's rights, and are subject to revision and amendment when they fail that purpose
- Equality and uniformity under the law is a goal, not a presumed achievement, and social failures to meet that goal are to be called out, protested, and discussed
- Problematic (criminal) behavior is caused by a combination of individual flaws and social contexts; it is a failure of the social contract that implicates both the individual's flaws and the social contexts that bring those flaws to fruition.
Police in this moral worldview are viewed as public servants, not reified authorities. Their purpose is to maintain the 'peace that is established by law', not to impose law as an end in itself. While individual police officers may themselves violate the law, that is superficial; the deeper problem is officers who (wittingly or unwittingly) use the law against society, not to promote society's interests.
With respect to the Chauvin case in particular, those in the first moral universe are inclined to think that Chauvin — as a veteran officer — was more deeply aware of the needs of the moment than any normal citizen, and that his actions arose from an unbiased, clinical assessment of the situation. They give Chauvin the benefit of the doubt that he believed his actions were necessary; they view Floyd as a criminal actor who was morally responsible for any harm that befell him; they see Floyd's death as unfortunate, perhaps even excessive, but consistent with the spirit of maintaining authority and social order.
For those in the second moral universe, Chauvin's actions were deeply inconsistent with the nature of the crime in question, and deeply insensitive to the rights and needs of Floyd (whom they see as a morally sound citizen). Chauvin (as a veteran police officer) should have been aware of the troubles Floyd was experiencing, and should have treated Floyd as a citizen to be protected first, and a criminal to be prosecuted under the law second. Chauvin is morally at fault for failing to attend to Floyd (and to the social contract he was hired to uphold) to such an extent that it resulted in Floyd's death.
This moral universe divide was further aggravated by the large-scale protests, which those in the second universe saw as a means of opposing unjust policing, while those in the first universe saw as mere disobedience to authority. And the situation was inflamed further by any number of Kohlberg stage 2 politicians and media personalities who felt they could make personal (political) gains by leveraging the divide.
Edit with respect to comments
The main critique of this answer seems to be that each side is going to have a slew of different understandings, leading to a multiple set of moral universes, not just the two outlined. The first part of that critique is perfectly true: in any group we will find people working at each of the six Kohlberg's stages, and while (say) stage 6 conservatives will have a different perspective from stage 6 liberals, both will be working from carefully thought-out abstract moral universals. Well, technically speaking, anyone still in stage 1 would lack any meaningful political perspective, so it might be difficult to distinguish conservatives from liberals at that lowest level. But set that aside...
However, even though the beginning of the critique is sound, the conclusion of a moral multiverse doesn't quite follow. Groups always establish a dominant narrative, and that dominant narrative carries the moral reasoning stage of the group as a whole. The dominant narrative in conservatism is stage 4, and has been since (at least) the Reagan era; the dominant narrative in liberalism has been stage 5 since maybe the 1970s. Subgroups might have different levels: The dominant narrative of Libertarians and old-school social conservatives is probably Kohlberg stage 5; the dominant narrative in Trumpism is Kohlberg stage 2 or 3; the dominant narrative in the Q-Anon movement may actually be Kohlberg stage 1. It may be that the dominant narrative in conservatism is on the cusp of changing to Trumpism, which will lower the overall moral level of the conservative narrative. But as of now, most of the leaders and adherents of conservatism are still clinging to that stage 4 narrative in which law and social order hold sway.