If the civil war destroyed states' rights, how did states manage to 'redeem' themselves and even de facto abrogate the Reconstruction amendments?

The South didn't abrogate anything. It weakened and eroded some things in some ways since the southerners were willing to constantly attack them, while the Northern states lacked the same degree of political will to perpetually fight back. So over time, the South was able to carve out compromise solutions like segregation that the North simply wasn't willing to "go to war" over. "separate but equal" obeys the letter of the law, and was only overturned much later based on the argument that it wasn't really equal after all.

The Civil War did massively destroy states rights in many ways, because it was the central question of the war: are states the ultimate authority, or the federal government? And the answer was the feds. So federal power massively expanded after the civil war, and was pretty much unchecked. Even now, only a small number of people like Thomas are even trying to hold back the feds in any meaningful way. Judge Roberts upheld Obamacare.

I would point to the nationalization of the "national guard" aka state militias:

Throughout the 19th century the Regular U.S. Army was small, and the state militias provided the majority of the troops during the Mexican–American War, the American Civil War, and the Spanish–American War. With the Militia Act of 1903, the militia was more organized and the name "National Guard" recommended. In 1908, the prohibition on National Guard units serving overseas was dropped. This resulted in constitutional debates within the U.S. government surrounding the legality of the use of the National Guard overseas, culminating in 1912 when U.S. Attorney General George W. Wickersham declared the 1908 amendment to be unconstitutional. The National Defense Act of 1916 contained a provision whereby the president could discharge National Guard members from the militia and draft them into the Army in the event of a war, allowing for their use overseas. This resulted in former National Guard members being discharged from the Army entirely (also losing their status as state troops) when they left service, so the 1920 amendments to the act defined the National Guard's dual role as a state and federal reserve force; the "National Guard while in the service of the United States" as a component of the Army of the United States could be ordered to active duty by the president, be deployed overseas if they so wished, and the Guardsmen would then revert to their status as state troops. The dual state and federal status proved confusing, so in 1933, the National Defense Act of 1916 was amended again. It finally severed the National Guard's traditional connection with the militia clause of the Constitution, providing for a new component called the "National Guard of the United States" that was to be a reserve component of the Army of the United States at all times.

Basically, the next time the US faced a significant war after the Civil War (WW1), the feds just basically federalized the national guard, and finally in 1933 dispensed with the charade of the national guard being anything other than a purely federal force.