"拥护共和政体的" can be translated as "pro-republican" or "supportive of the republican system".
"Pro-republican" directly conveys the idea of being in favor of or supporting a republican form of government.
"Supportive of the republican system" is a more descriptive phrase that explicitly states one's stance in favor of the republican political structure.
Both expressions are appropriate depending on the context and the level of formality required.