'Savvy' is a noun, so we are just forming a compound noun ( noun + noun, a common process) with ' political savvy ' (a very common compound) and 'technology savvy' (one I have not heard, but one I would have thought would emerge as 'techno-savvy'). The second of your proposed antonyms is the correct structure ('politically incompetent'), but not antonymous because it is adverb + adjective. The antonym would be ' political incompetence '.
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