A good case could also be made that Capitalism is also antithetical to the Constitution. Do you support the court martial of those who express a belief in Capitalism?
I do not agree that a good case could be made that Capitalism is antithetical to the Constitution. Therefore the 2nd question is moot.
Capitalism respects private property rights, which are enshrined in the Constitution and Bill of Rights via protection against illegal searches/seizures in the 4th's protection from searches and seizures and the 5th Amendments prohibition against taking property without due process. It's also in the 3rd Amendment, where the government can't force soldiers into your property precisely because it's considered your property. I imagine you know this already though Sir, being my senior and all.
Furthermore the Constitution is based on Natural Law/John Locke's teachings, and there ain't no way that Communism and Natural Law can mix.
Constitution/Natural Law = If I go into the woods, and gather a handful of acorns, then that's my labor and I keep it
Communism = If I get a handful of acorns I distribute my acorns (property) to everyone else equally, compelled with force from my government if necessary.
Any system that disrespects private property rights and individual freedom is not compatible with the Constitution, nor the Federalism it contains. And likewise violates an oath to preserve and defend it. There's nothing in a Capitalistic system that denies any part of the Constitution.