RE: Depends on whether the federal government of the time had adhered to the ideals behind the founding and left the South alone
Well, if the Federal government allowed the South to secede, of course we would not have a United States ( as we know it today ).
We would have a United Northern States and maybe, who knows? A Confederate States of America...
I would also surmise that we would probably have something like a continent like Europe, consisting of independent countries big and small.
As for Slavery ... it was a dying institution anyway and would go the way it did with the South American and Caribbean countries, albeit, it would have taken longer to die out in the South.
No, in 1860 slavery was prospering as never before and average slave prices the highest ever.
That's what gave Confederates confidence to build their new country specifically on slavery.
And nothing short of an existential crisis was ever going to change that.
What sort of crisis?
Well, if Europeans dictated that Confederates could no longer export slave-produced cotton & tobacco, that would make a huge crisis.
But the chances of it happening anytime in the 19th or 20th centuries are slim to none, especially if Imperial Germany had won the First World War.