Why were blacks still victimized in the Northern states after slavery's abolition?

I can understand why the former Confederate states still discriminated against blacks starting from Reconstruction, but why did the North?

Before we get to formal Reconstruction, we can examine some actions of the federal government immediately following winning the U.S. Civil War as a model for how the nation was to treat free blacks. We immediately encounter General William T. Sherman's Special Field Order No. 15, popularly referred to as "40 acres and a mule", which set aside certain lands for free blacks to "possess" and govern themselves thereon. Tens of thousands of free blacks traveled to and settled on the "promised" land. Within 4 years the blacks had largely been removed from the land again, which was in large part was returned to pardoned property owners in the South. The federal government policy objectively used the then free blacks both for military and political purposes until those free blacks were no longer politically and militarily useful to the state.

Sherman's Field Order No. 15

The immediate effect of Sherman's order provided for the settlement of roughly 40,000 blacks (both refugees and local slaves who had been under Union army administration in the Sea Islands since 1861). This lifted the burden of supporting the freedpeople from Sherman's army as it turned north into South Carolina. But the order was a short-lived promise for blacks. Despite the objections of General Oliver O. Howard, the Freedmen's Bureau chief, U.S. president Andrew Johnson overturned Sherman's directive in the fall of 1865, after the war had ended, and returned most of the land along the South Carolina, Georgia, and Florida coasts to the planters who had originally owned it.

Although Sherman's Special Field Order No. 15 had no tangible benefit for blacks after President Johnson's revocation, the present-day movement supporting slave reparations has pointed to it as the U.S. government's promise to make restitution to African Americans for enslavement. The order is also the likely origin of the phrase "forty acres and a mule," which spread throughout the South in the weeks and months following Sherman's march.

Grouping entire populations into North and South is a perhaps improper here. It implies that all of the actual people in the North that were not also politicians and particularly the ruling class practiced discrimination against blacks. We remember John Brown and his sons before Reconstruction and the Boule after Reconstruction. Meaning people who self-identify with or are considered socially or politically black or white does not mean their politics are reflected in how an individual or group might blanket cast an entire "race" as having the exact same tendency to discriminate for or against a different "race". "Race" is in parenthesis because "race" is not defined by Public Law in the United States, see Is the term “race” defined by Public Law enacted by Congress of the United States there are nations where "race" is not used within governmental document, and there is no universally accepted definition of "race" either among individuals, scholars, or under international law.

Isn't it inconsistent for Northern whites to have believed earnestly in, and championed, slavery's abolition, but remain racist against blacks?

As with the previous inquiry, I would caution against accepting the premise of "Northern whites", as if that were a monolithic group having a single mission statement, which is not the case.

Even championing abolition does not equate to a purely charitable motive for seeking abolition. Nor does the mere abolition of "slavery" mean that the lowest rank of "white" person in the society is still not ranked above the highest "black" person under the global government of white supremacy. Joanna Brooks mentions being influenced by a certain definition of "whiteness" by Noel Ignatiev and John Garvey who are affiliated with the Race Traitor project:

The white race is a historically constructed social formation. It consists of all those who partake of the privilege of white skin in this society. Its most wretched members share a status higher, in certain respects, than that of the most exalted persons excluded from it, in return for which they give their support to a system which degrades them.

While it is important here to note that "race" is also not related to science, though the period the question asks about is the beginning of "scientific racism", when exactly such a scientific definition was attempted, failed, but was widely accepted nonetheless.

There’s No Scientific Basis for Race—It's a Made-Up Label

Morton thought he’d identified immutable and inherited differences among people, but at the time he was working—shortly before Charles Darwin put forth his theory of evolution and long before the discovery of DNA—scientists had no idea how traits were passed on. Researchers who have since looked at people at the genetic level now say that the whole category of race is misconceived. Indeed, when scientists set out to assemble the first complete human genome, which was a composite of several individuals, they deliberately gathered samples from people who self-identified as members of different races. In June 2000, when the results were announced at a White House ceremony, Craig Venter, a pioneer of DNA sequencing, observed, “The concept of race has no genetic or scientific basis.”

Scientific Racism Isn’t ‘Back’—It Never Went Away

It was Darwin’s half-cousin Francis Galton, who coined the term “eugenics,” and his theories of biological determinism that bridged Darwinian natural selection and human beings. Soon Herbert Spencer’s phrase “survival of the fittest” became the zeitgeist of the era, and the logic of Social Darwinism took second place only to capitalism as the American civic religion. The moral imperative for the weak to perish and the strong to survive was applied to the economy, international relations, politics, social classes, and the hard sciences. Just as America would rise above and crush the weaker nations of Old Europe, so too would the races settle into a natural order in which the dominant ethnicity of the elite class (Anglo-Saxon, Germanic, and northern European) would prove with finality its superiority over the lesser peoples (everyone else).

The overall point of the answer is that white supremacy is a political construct, a social formation by classes, a business; where an individual may or may not be "white" (see What are the legal requirements in the United States for being recognized under federal law as “white” or a “white” person?) though still profit from the business of white supremacy, in any era businesses adapt to or innovate the market, create new products, re-invent themselves. White supremacy shifted, or using a term whose origin is rooted in the notion of some modern scientists, adapted from application of physical chains to application of mental chains, i.e., academia, and continues to adapt today.

What If Reconstruction Hadn’t Failed? The pervasiveness of white-supremacist ideology in academia gave license to Jim Crow efforts for decades after the Civil War.

In this view, President Andrew Johnson—who did everything he could to sabotage efforts on behalf of the formerly enslaved, and after his impeachment in the House of Representatives, escaped removal from office by one vote in the Senate—was portrayed as the hero who had valiantly attempted to save the country from the specter of “Negro Rule.” The men who opposed him were considered dangerous “radicals” aimed at upsetting the racial hierarchy and making inferior people citizens of the United States. Johnson, who was barely educated himself—he learned to read in his late teenage years and to write just a few years later—was held up as one of the country’s great presidents.

The urgency to limit black advancement and create doubts about the efficacy of black citizenship was derived from the doctrine of white supremacy. Blacks of the era saw Birth of a Nation for what it was, and organized protests in various venues where it was screened. But, as noted, it was not only that movie’s presentation of Reconstruction-as-horror-show that had to be confronted. The early written history of the era put the weight of academia behind crude formulations of racially based power politics; making the pronouncements of blacks’ unfitness for citizenship a matter of social science and, for some, pure science. These writings served late 19th-century and early 20th-century political and social arrangements—disfranchis*m*nt, Jim Crow, and, for extremists, lynching. Casting doubt on blacks’ innate capacities, they gave license to question whether African Americans should, or could ever, be successfully incorporated into the American polity. Very importantly, it was to be left to whites to decide the question when, and if, blacks would ever be eligible to exist with all the attributes of citizenship in the United States. Blacks resisted this idea in the streets and in scholarship.

As to your first question, I think it's a combination of:

1) Insularity / lack of familiarity with other races / fear of the unknown and the tendency to listen to alarmists / the continuum going on up to racism. Whites saw blacks being very different, in many cases ignorant and living primitively or in poverty and presumably (in their minds) that was because they weren't naturally fit for white society, and not fit for any but menial work.

2) Concern over jobs - mostly for urban dwellers working for someone else, IOW, not just on in a small town with people you know or on the farm working with your sons. People thought that blacks would be more likely to accept lower pay for the same job, which led to some acts of violence or vandalism against blacks and their dwelling places. Even back post-war, there were of course economic ups and downs, with jobs sometimes hard to find, so additional competition was not welcome.

Equality is a process or continuum, not an on-off switch. Northerners in the 1800s both believed that slavery of a human being was wrong, and felt that a natural racial hierarchy existed. Poles, Irish, and Italians were considered of a lower racial 'tier' than white Anglo-Saxon Protestants until the 20th Century, not to mention the lower status of Asians, Hispanics and Middle-Easterners.

If you remember the 2000's, one of the intermediate steps in the acceptance of gay rights came in the form of people saying "They can do whatever they want in their own homes with consenting adults, just don't hit on me or make me look at it." This intermediate racism strikes me as very similar. They felt blacks should be allowed the right of self-determination as long as they kept to their own communities. Only over time, exposure, and in some cases, forced desegregation, did white Anglo-Saxon Protestants finally come around to the idea of racial equality.