Did the Civil War Basically End in 1865?

For about 300-odd reasons, yes.....the war ended on 9 April 1865.  For most folks, depending how rural you were living....you probably didn't know about it for another week or so. 

For about the next five years, the former Confederate states go through a 'rehab' period, and things are kinda laid out as 'recovered'.

In the spring of 1898, I would consider all issues resolved because of the unified US engaging on the US-Spanish War....briefly lasting four months.  At that point, southerners returned with parades, and medals....as part of the national campaign.

The first 'true' southern President?  Wilson.

Participation in WW I?  Another element of the unification.

So why all the flag-waving of the Confederate flag....long gone for almost 155 years?  I would suggest that around one-third of the general population sees the conclusion of the war in a different aspect. 

Some can point toward members of their family having been in the war.  Some can point toward destruction of their local town.  Some simply want a piece of something that lasted less than five years.