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Conservatives aren't necessarily reactionaries.
Literal
Conservatism [gen-の] people [subject-が] not-necessarily reactionists [quotative-とは] doesn't-limit.
The standard 必ずしも~とは限らない frame for 'not necessarily X.' 必ずしも is an adverb that can only appear with negatives — paired with とは限らない, it softens the denial from 'never is' to 'isn't always.' 反動主義者 is a compound of 反動 ('reaction, backlash') + 主義 ('-ism') + 者 ('person') — a polemical political label.