Does the Civil War still matter? If you accept the premise that the conflict is America’s defining event, then absolutely it does.
In 2012 I gave this response in an interview in which I repeated my response to a question on a staff ride about the Civil War’s relevance to today:
The Civil War is the defining event in this country’s history – to fully appreciate today’s United States, we must understand the events of 1861-65. The war (and its outgrowths in the form of the 13th, 14th, and 15th Amendments) forever changed this country and shaped it to this day. I also made the point that 5,000 Hispanics served on both sides in the war (including Admiral D.G. Farragut and Lt. Col. Julius Garesche, killed at Stones River), and that the liberation of African-Americans in the Civil War ensured the freedoms for all races and sexes that exist today. Every person in the United States is affected by the Civil War, directly or indirectly, every day— something that should be remembered.
As an extension of the above, I’d note that while the nation was founded in 1776, it was in many ways re-founded in 1865. The Civil War’s end and resulting 13th, 14th, and 15th Amendments reshaped the nation and established a political and social course with effects that Americans are still grappling with today. Details of this re-founding and its elements are in this post of mine from 2015.
Lastly, the identity, and in many places the physical geography, of much of the country, especially the Southeastern United States, is heavily influenced by the war, its activities, and the memory thereof.
Does the Civil War still matter? Absolutely—and it will as long as the United States of America exists.