On February 4, 1861 the Confederate government was proclaimed. On March 3, 1861 Tzar Alexander II freed the serfs. Between the Confederacy and the Russians someone was going in the wrong direction and it wasn't the Russians.
Let me try this again:
We believe in free speech. Most of us disagree with many of the ideas being promoted with this free speech - like forcing institutions to pay for contraception and abortion against their core principles.
Should we oppose free speech because of how some are using this freedom? If not, then it is philosophically consistent to support the right of southern states to secede, regardless of the reasons for said secession. Then you may have the debate about slavery and if it is incumbent upon a neighboring country to fight a war of liberty against a slave holding neighbor.
So - were I Lincoln, I would have allowed the secession - such being the right of free states. Then attacked the newly formed Confederacy in a war of liberation on behalf of the slaves. Once defeated, the CSA could petition for readmittance, and the USA could either accept or reject that petition.
This is fully consistent with a libertarian viewpoint IF that viewpoint allows an war of liberation against a neighboring country.