Why Civil War re-enactments?

In the South, it seems that your whole family status revolves around your family's involvement in the Civil War.   Elsewhere, nobody seems to care about your family's war record for any war. (Unless it is around a Vet or Nov 11th.)

Reenacting the American Civil War began even before the real fighting had ended. Civil War veterans recreated battles as a way to remember their fallen comrades and to teach others what the war was all about. ... Modern reenacting is thought to have begun during the 1961–1965 Civil War Centennial commemorations.

Because they require much simpler forms of weaponry. No tanks, no aircraft, there was very little warfare at sea.  Battles took place with much smaller footprints and they were short, lasting only a few days instead of long, extended campaigns.

You are understating the emotional impact that other wars besides the civil war had. I can name far more American WW2 and Vietnam films off the top of my head than I can for the US civil war. 

Unlike the other wars you mentioned, the Civil War was fought in the US, in the places where Americans still live.  Even WW2 had little direct impact on the country by way of combat operations.  Additionally, the Civil War was a defining moment for the country more so than arguably all of the others combined.  There is also the fact that it was the bloodiest war in US history.  

Re-enacting historical periods offers a way to understand them better by experiencing what the people went through at the time - it helps society to learn about itself.

Americans romanticize the antebellum period partly because of the fashions of the era, and what they fantasize as being "a simpler lifestyle" compared to their current fast-paced but boring existence.

Controversy adds to the mix: Lincoln was the first President to be assassinated - a society game-changer. Slavery was accepted and was commonplace - not that it was right or wrong; it existed nonetheless. The moral issues were debated and still are.

It was the only time the country was divided and it was the only time when families were politically divided with brother fighting against brother.

The other conflicts you mentioned were ones that defined someone else's history. The Civil War examines America's own history.

The Civil War isn't the only historical era that has re-enactments. You should visit a Youtube channel called the Townsends to see historically accurate re-enactments of 18th-century life.

https://www.youtube.com/user/jastownsendandson

Because they are reenacted on the battlefields where they occurred. Those other wars/battles occurred overseas. It wouldn't make sense reenacting the Battle of the Bulge in Pennsylvania.

The entire Civil War took place in the US. I'd feel condescending by elaborating on this. 

Recent wars aren't as romantic or interesting. 

The people who do them can't afford plane tickets to France, Italy, Germany, etc., but they can afford to drive just up the road.