Could this be explained as a classical definition of cognitive dissonance? Instead of being consciously aware of their views, they hold contradictory doublethink (that they are patriots of democracy while supporting a fascist), usually inculcated by right wing media that is fed to them.
If you bring up the logical contradictions, it doesn't change their mind as they hold the beliefs to be true and "rational" in their mind as it supports their worldview.
I wouldn't classify them though as protestors, who seek to change the societal Zeitgeist and public policy / laws through nonviolent means. Rioters would be a more accurate description of the January 6, 2021 mob.
As far as their philosophical leanings, they don't appear to ascribe to classical philosophy, but hold fast to a narrow and myopic interpretation of Christianity that has been hijacked by conpeople under the guise of the "Moral Majority". They follow the Bible on social media but rarely read more than the snippets required during church service. Spiritual in Name Only. Theatrical performance over substantive introspection. The end result is a hollow void that they believe is filled with a Holy Spirit but is instead an aetherial chamber of hollow half-truths and hot air.
I want to believe we can change their minds, but I am not optimistic about it as the brainwashing is quite significant. They aren't LARPers because they aren't roleplaying; to them it is anything but roleplay, they truly believe in it regardless of how far away from the rest of us that they really are.