I don't think the offensive thing is his action itself (as people said, it's his right).
But it's the fact that our cultural climate in the US is so systemically anti-American. In earlier days, such an action was unthinkable, not because the law said it was wrong (it didn't) or that there was some civic religion binding everything together (some admittedly saw it and still see it so to this day).
America back then wasn't so distant. America wasn't the IRS, FDR, Buzzfeed, Cops, or Beyonce. America was our neighbors, our churches, our Wednesday meetings at the Elks Lodge. To not put the hand over the heart was almost a breach of that sacred, organic brotherhood.
The more we've distanced ourselves from real community, the more incidents like this will occur. Why put the hand to the heart when there is no real America?