The Continental Congress voted on 2 July, 1776, to declare independence, and ratified the Declaration of Independence on 4 July.
Four score and seven years later, we were engaged in a great civil war.
This poster, displayed at the October 2006 reenactment outside Stockton, Illinois, gives an idea of how great that civil war was.
On 3 July, 1863, the rebellion became militarily untenable, with Meade and Hancock breaking Pickett's Charge at Gettysburg, and Vicksburg garrison commander John Pemberton asking Grant and Sherman for terms, reckoning that his former colleague Sam Grant would be disposed to be magnanimous on Independence Day.
"Militarily untenable" is not the same thing as "crushed utterly," and there were still ways in which rebellion could have lingered as guerrilla warfare or a low-level insurgency, even after the last rebel armies in the field stacked arms in April 1865. And yes, to this day, the South is different from the North.
And yet, does anyone seriously expect North Carolina to leave the Union over its bathroom policy, or Mississippi to do so over its religious freedom law being contrary to the Establishment Clause (let alone that it's a form of nanny-statism?)
Reasons for disagreement? Yes. Causes that Impel them to the Separation? I'm not persuaded.