As this topic once again begs the question..."What's the POD?", I'll say, for conversation's sake, that there is a POD with the range of the Trent Affair on one end and Antietam on the other. Another thing to clarify is that barring a POD that extends well before 1860; the South won't be let go without a fight as all the major Republican candidates were Unionists. So with Lincoln as President and a POD in the range given above we can be assured of a few things. 1.) In order to win the South needs European intervention by way of political recognition, breaking the blockade and large amounts of military supplies. 2.) The Union will declare war on any European power that recognizes the South prior to a final treaty. 3.) The Union will focus on destroying the Confederacy and fight defensively in along the Canadian border. This follows the spirit of Lincoln's belief that the Union fight only one war at time and plays to the US's strengths. 4.) The North will fight until it is truly defeated or until the Republicans loose control of Congress and are thus forced into a negotiated peace (this is more likely and I'll assume the Democrats do very well in 1862 and force a peace in May of 1863). 5.) The peace treaty will not be overly harsh and Britain will gain only a few square miles of land along the boundary with Maine as well as Hawaii. The US will be forced to recognize the French puppet government in Mexico.
Also very likely is that the US will pass a few bits of choice legislation during the period between the POD and a final peace treaty. 1.) Homestead Act that includes settling free negroes on land paid for by Abolitionist Societies. This will pass by a slim margin due to an unlikely alliance between abolitionists and urban democrats who want blacks removed from eastern cities. 2.) Repudiation of the Fugitive slave laws as well as compensated emancipation. These will cause future friction but at the peace Treaty Britain can not in good conscious ask that they be overturned. 3.) First move towards an amendment barring secession. 4.) Transcontinental railroad act with the line running from St. Louis to San Francisco.
The peace treaty will allow each border state to vote on their status. In Delaware the vote is overwhelmingly pro-Union. Maryland is bitterly divided but Union control of the Chesapeake Bay had already forced many slave owners to head South so the state votes to remain in the Union. Kentucky narrowly votes to go to the Confederacy which leads to decades of internal strife. Missouri, with the promise of a trans-continental railroad, votes by a wide margin to stay in the Union. The Indian Territory and Confederate Arizona (at France's demand) also go to the Confederacy. Britain evacuates San Francisco and refuses to push the Oregon issue as they fear moving the border back to the Columbia will only lead to future trouble as American immigrants pour in (something that already threatens in New Caledonia).
Now that I've gone a bit over board with the background...we can look at Northern culture post Southern secession.
The North was bigoted and racist, but no more so than the rest of the world at the time. In fact in that regards it was a pretty decent place. That's why even in OTL millions of people made the decision to move there despite the prejudice against them. This will still hold true. A bad recession immediately following the war will slow immigration a bit but not for long. The Dems will control Congress for a little while and probably win the 1864 presidential election, but their constant cozing up to the South and refusal to raise tariffs will hurt them in the long run. They'll block an amendment to end slavery but the institution is dead in the North. Even the Democrats won't be dumb enough to oppose an amendment barring secession. Anti-immigration legislation will fail because in order to keep wages low, especially since the Homestead Act, the Northeast will need immigrants.
The North will be more militarized, but it might end up similar to Switzerland in that regard. The distrust of a standing military won't go away over night, especially if some dill weed like McClellan interfered with the Federal government during the period leading up the the end of the Civil War. Also, lessons learned from the breaking of the blockade will see an increase in the size of the Navy.
Overall the US will be much more liberal in regards to civil rights. During the brief interlude in which the Dems play nice with the South, states will once again pass Personal Liberty laws and attempts to recapture slaves will lead to violence. Except for a few states in the Mid West blacks will be rather well treated in the North. Even those Mid West states will give up on racism far earlier than OTL.
Music will still have black minstrel influences and thus jazz, which might end up being a form of "freedom music." In plays the lazy abusive plantation owner will become a cliche character along with the scheming European banker/politician/aristocrat (who also abuses the working class of his country). The Labor movement could go either way. The loss of the South won't make the average worker's plight any worse, and a more open land ownership policy in the West will work to make it better by increasing wages. The Indians will have it worse off in the short run but better in the long run. They will be swamped by numbers faster and have fewer or no reservations, but this could lead to a more equal land distribution system similar to what I envision for blacks. This will give individual Indians their own privately held land and do away with the corruption of the Reservation system. Furthermore with blacks leading the way and being larger in numbers there may be less conflict over all as blacks historically worked better with Indians and race will be less of an issue (this will lead to citizenship for Indians at much earlier date as well).
Benjamin