False dichotomies fuel political discourse, too.
"If you don't like the police, next time you're in trouble, call a crackhead!"
"If you don't support the troops, feel free to stand in front of them."
"If you oppose the COVID-19 shutdown, it must mean you want people to die!"
"If you don't like Obama, you must be racist!"
"If you don't like Trump, you must be a commie!"
The left/right split is the greatest false dichotomy of all.
Progressives and conservatives both seek greater centralization. Conservatives are more prone to present their ideas as false dichotomies. Progressives like to present paradoxes with centralization being the only solution to the paradox.