The best strategy is to ignore the flag. This situation is similar to one where the government makes a law where somebody can't say a certain word. Sure enough, some punk will want to say it.
However, the Confederate flag should be taken down from government buildings. The reason for this action lies in the fact many of these states have a large black population, and a majority of them don't like the flag. Well, at least they don't want to displayed by the government.
Just a side note about the 1950's and racism: Not many people will believe or acknowledge who the southern racists were back then. The south was run by democrats, and they were the ones who were determined to keep blacks and whites separate! It's funny how since integration became the norm, the democrat propaganda machine has been thrown into overdrive, blaming all the southern racism on the Republican party.
Actually, Eisenhower did the more for Civil Rights than Kennedy or Johnson. The reason blacks flocked to the Democratic party was due to their support of massive government aid programs. Actually, they switched sides when Rooselvelt was in office, but Johnson was the one who put in the programs blacks really liked and came to depend on. I'm not sure how much support Kennedy or Johnson got from blacks due to civil rights alone.
Note, even though I think most Republicans supported civil rights measures, southern whites began to switch to the Republican party after 1968, maybe earlier. Possibly because Nixon promoted a southern strategy, one which later Reagan supported. This strategy accepted civil rights, but besides that, was reluctant to give too many concessions to minorities. As for Nixon himself, he was actually a mild closet racist, but not as much as most white southerners, and he didn't really care about southern traditions, seeing as he was from California.