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Conservatives are quick to tell you to act within your station.
Literal
Conservative [na-な] people [topic-は] quickly station-appropriate [adverbial-に] behave-(imperative) [quotative-と] say.
Dense with cultural content. 分相応 (ぶんそうおう) is 'befitting one's (social) station,' a traditional concept that was culturally enforced in pre-modern Japan and still echoes in conservative/traditionalist rhetoric. 振る舞え is the plain imperative of 振る舞う ('to behave, conduct oneself'), embedded as a direct-ish quotation inside ~という. すぐ (~ます) here means 'immediately,' 'readily' — a slight negative flavor in this context.