The integration of large language models into political discourse analysis creates new opportunities for comparative research, policy analysis, and civic technology, while introducing material risks for democratic accountability. This paper argues that cultural adaptation is a prerequisite for trustworthy deployment of large language models in political communication across diverse linguistic and institutional contexts. Current systems remain shaped by English dominant data, uneven multilingual coverage, and assumptions grounded in a narrow range of political institutions and discourse conventions, producing systematic errors when applied across cultures. We formalize cultural adaptation across translation, discourse, and ontology levels, identify recurring cultural failure modes in political NLP, and propose an operational evaluation matrix grounded in cultural fidelity, calibration, and democratic safety. Building on political text analysis, sociotechnical auditing, and cross cultural pragmatics, we outline methodological pathways including participatory dataset development, culturally aware transfer learning, and benchmark design that makes cultural adaptation empirically measurable. We conclude by clarifying governance constraints and scope conditions under which culturally adaptive political NLP can support democratic legitimacy.