Interesting. Conversely broad-minded genuine conservatives and broad-minded genuine liberals are not at loggerheads. In fact, a person can be both liberal and conservative at the same time.

The same pattern can be seen in other areas. For example, an extreme hater of religion who has a dogmatic materialist philosophy is little different than an extreme religious fundamentalist. Yet open minded atheists and open-minded religious people often get along well and find common ground.

Maybe instead of emphasizing our differences of opinion we should emphasize our degree of awareness and appreciation for the profound miracle of existence and our love and respect for our fellow beings.

IMO horseshoe theory is severely oversimplified because it assumes that as liberal ideologies become more extreme they lean towards authoritarianism, when in reality we see extreme libertarianism coupled with left (anarchism) and right (anarcho-capitalism) ideologies, and that would make the shape more of an hourglass.

It also only assumes only two axis, economic left-right and governance libertarianism authoritarianism. You could very easily throw in culture (individualist-collectivist), or progressivism ( traditional-progressive). In fact, without some of these dimensions certain political ideologies become difficult to map, for example fascism which is very authoritarian but is neither left nor right economically, so a line at the authoritarian end of the graph could represent a fascist regime.

The 8 political values is becoming more popular but has the same problems as the other methods used in political science. [8values.github.io]