This ruling makes sense to me. The Confederate Flag is, inter alia, a symbol of rebellion against Federal power. Even as a heritage symbol, which is how the Sons of Confederate Veterans want to use it, displaying it aligns one with the historical cause of rejecting the Federal government outright where it overstepped the community's understanding of its constitutional bounds. The Federal courts' extraordinary power over every aspect of American life follows directly from the defeat of that cause and the consequent Reconstruction's 14th Amendment.
So when the SoCV went forward with a lawsuit claiming the right to force the government to accept the symbol, of course the courts are bound to reject that. The liberal wing of the court was united here, joined by Justice Thomas. The article mentions that he is 'the court's only African-American' in a way that suggests this was a causal factor, but Thomas is surely correct as an originalist. The purpose of the Reconstruction amendments was to suppress just this particular political expression. For, as von Clausewitz reminds us, war is only politics by other means.