It's no accident that the shows that people like Greene bloviate on tend to have names like "Real America's Voice." These are the same sort of people that trot out the superficial "we're a republic, not a democracy!" thing when they get out-voted as a reason to ignore that result. What it all comes down to is that they are the Real Americans, with the proper values and objectives, that's what really matters, and any opposition is un-American, "socialist" or "communist," certainly ungodly. In essence, they feel that they own America, so it doesn't even really matter if they lose a vote, they're still entitled to act as if they won it. Ownership imposes an obligation to maintain itself, so just about any tactic for that righteous maintenance is by definition justified; and there's no obligation to share, so everyone else who wants in can just go hang.
If America changed to encompass things they don't agree with, it's not America anymore.