How were they received by wider Washington society? Were they blamed for the war? Were they still respected? Were they ostracized? Did they repent for their role in the Civil War, or refuse to recognize their place in history?
The Supreme Court wasn't quite as sacrosanct or dependent on the personalities of individual Justices, as it is in the hyper-partisan post-Souter era.
The scotusblog is a tremendous resource for questions like this. To show how the Supreme Court was seen back then, consider this article which delves into Lincoln's court packing during the Civil War: http://www.scotusblog.com/2013/07/the-first-court-packing-plan/
Initially, Lincoln wished to raise the number of Justices to 10, to help enact his agenda:
The legislation came just as the Court was considering a major challenge to Lincoln’s blockade of southern ports. In a five-to-four decision handed down right before Field began his duties, the Court upheld the blockade and handed Lincoln a major victory. By adding a Justice, the Republican Congress reminded the Court at a critical time that it had the power to affect its membership.
Republican efforts to adjust the Court to accommodate political realities did not end there. In 1866, just after the war ended, Congress enacted legislation reducing the Court’s size by attrition to seven, thereby preventing President Andrew Johnson – a fierce opponent of congressional Reconstruction plans – from nominating any Justices. [...] Three years later, with Johnson out of office, Congress returned the size of the Court to nine Justices, where it has remained ever since.
So as you can see, congress was quite happy to raise the number of Justices to 10, then lower it to 7 to spite Johnson, then raise it back to 9 again, in the space of only a few years.
FDR was infamous for packing the courts to help push his New Deal, in such a way that provoked generational backlash from the Republicans. FDR nominated many judges because of their economic liberalism. Yet as the civil rights movement dawned, many were revealed as socially conservative.
As for the Justices named (all of whom received numerous honors, even after the civil war):
James Moore Wayne was remembered and admired more for remaining true to the Union, despite being a Southerner. He was also one of the longest serving Justices ever, and died almost immediately after the war ended (1867), which is what partially enabled Congress to lower the number of Justices down to 7 from 10, to screw Johnson.
Further showing how different things were back then, after the Civil War, Samuel Nelson took a temporary leave from the bench at the behest of President Grant, to serve on a commission investigating damages for Confederate piracy during the Civil War, during which he died. There is absolutely no way that a modern Supreme Court Justice would temporarily step down from the bench to oversee another function.
Anyhow, where Samuel Nelson is concerned, he received much more flak for dissenting as to whether it was constitutional to blockade the South than he ever did for Dred Scott. But again, not even remotely ostracized.
Robert Cooper Grier sided with the Lincoln administration on the constitutionality of the blockade, which again, was considered much more important. He also died shortly after the war ended, in 1870, by which time the country was struggling with Reconstruction.
In short, like millions of others in the North, the three Justices were not pro-abolition, yet were definitely pro-union, and that was the much bigger issue of the time. All of them died between 1867 and 1873. Although Samuel Nelson did attract some scorn, it was for his dissenting opinion on the blockade of the South, not for anything slavery related.
All available biographical evidence suggests they remained part of Washington's societal elite, and their exact identities and ruling on Dred Scott matters more to us, than it did to Reconstruction Era Americans.
It is highly anachronistic and misleading, to try and project the current sensitivity about the Court back to the 19th Century. Imagine how people would react, if in order to secure a decision on Obamacare or Immigration, a Republican-controlled Congress simply added a couple more seats, or removed a couple if Hillary were elected.
It's hard to emphasize how little these men's lives were affected by the ruling in that one case. Nor would a different ruling have prevented the Civil War. It might even have hastened it. What was more important to their contemporary peers, was their pro-Union beliefs.