I'm referring specifically to the social right wing. The social axis specifically deals with authoritarianism vs libertarianism. More control vs less.
The economic right wing and left wing, no, are not inherently authoritarian.
left/right wing terminology is really weird in american politics and i'm p sure things were interpreted in that context
i don't know if this is the
best summary possible but i think, generally speaking, [in america] right-wing tends to value order/tradition over liberty (see: counterterrorist surveillance, voter id and similar measures, 'religious freedom' laws, etc.), left-wing tends to value equality over liberty (see: 'tax the rich', social safety nets, civil rights regulations+other anti-discriminatory laws, etc.)