whether violent criminals perceive themselves as espousing a certain ideology and adopting a symbology while carrying out their violence does not automatically make the ideology or the symbology associated with the violence carried out allegedly in its name. this holds for the US flag and constitution as much as to communist symbols and writings. associating any of them with atrocities carried out in their names is propaganda, because neither the symbols nor the writings support those atrocities, which is significantly unlike e.g. the fascist, nazi and bolsonaro symbology and writings, that do support, endorse and promote atrocities.
so if a gun-armed person carries out a terrorist attack in a school wearing a US flag or a communist icon, associating those icons with terrorism would amount to making the same mistake that the terrorist made, whereas if the person carried a swastika, the association would not be a mistake. hatred is inherent to nazi philosophy, but not inherent to communism. does that make sense to you?