A rather inaccurate, if not rabid, explanation of everything.
Lincoln did care about slavery before he was elected -- he spoke and wrote about it. It just wasn't his only issue.
Perhaps true that most of the signatories cared more about their way of life than states' rights, but it's unfair to claim that NONE of them cared about ANYTHING but profit. Some were probably cared deeply about states' rights, just as some of the founding fathers did in their skepticism about federalism.
In the CSA, there were definitely states' rights, though they often fell behind the pressing fact of the war. Those states' rights were why so many local militias were kept home by governors when the CSA government wanted them all in the field.
They (Southern leaders) DID have a strong influence on the constitutional convention, but so did other factions. Every faction fought for their own way of life and the things that were important to their state -- that's as true for Massachusetts as it is for Virginia or South Carolina. That opposition of viewpoints is why getting the constitution written and ratified was so hard and why it contains LOTS of compromises -- the electoral college, the bicameral legislature (with different representation), the 3/5 clause, etc.
Again, Lincoln DID care about slavery, even early on. He just wasn't willing to rip the country apart solely about slavery -- he was willing to let the issue work its way through the 'body politic' and eventually into law or amendment. He cared MORE about union than about slavery because he knew that was an existential issue -- win or the Union ceases to exist. Additionally, he tried to work within the rule of law, even during the war. That being the case he COULDN'T outlaw slavery by presidential order and trying to do so would have caused internal revolt and probably the defection of some Northern border states (MD), etc.
Finally, while some modern politicians do use states rights as an arguing point on today's issues it doesn't follow that it's disingenuous to do so. That pesky ol' Constitution does still reserve certain rights to the states, certain to federal, and all the rest to individuals. Further, much of our system of laws, budgets, etc. is specifically set up with states rights and priorities in view. When the federal government tries to overrule that, it gets messy fast -- Obamacare is a recent example -- forcing 50 states to do roughly the same thing within 50 different sets of laws and policies.
So, yes, states rights are "still a thing" and not just political rhetoric.
Go read the actual document regarding seccession; The North banned slavery via states' rights and the South saw the Federal government allowing this to be a violation of its own authority, and their paranoia erupted when Lincoln became president because his ideology matched the north rather than the south, even though he didn't care about slavery. If anyone in the Confederacy cared about States' rights, it was the soliders, but absolutely none of the signatories or politicians involved gave a shit about anything but profit.
In an alternative universe where the Confederacy conquers the entirety of otl USA there are no states rights, only CSA ideology. The idea they cared at all about states rights is silly if you know their history. They dominated the Federal government early on and consistently forced their ideology upon other states via Federal law when it suited their benefit, they cared exclusively about their way of life which included slavery.
Abraham Lincoln didn't give a shit about slavery, he wanted unity and had 0 intention of getting rid of slavery because it would have divided the country. He only got rid of it as a tactic of war, and the proof is in the fact that the states that had slaves AND didnt rebel weren't forced to outlaw it. If you believe states rights had anything at all to do with the civil war, you have plenty of reason to; it was used as propaganda to get Southerners who wouldn't fight for slavery to fight for the southern rebellion, and it's been used by modern politicians to support modern ideologies, but it had absolutely nothing to do with the south seceding. The South thought it was a right to own people, not that states had rights themselves.