You're misusing a couple things here in philosophy. Paradoxes do not exist in nature because nature is the only complete and consistent system within itself.

All logical systems will have a logical end-point. This is Gödel's Incompleteness Theorem. All logical systems can be either complete or consistent, but never both. Meaning: either you have a logical system that covers all things and gives inconsistent results (generating paradoxes in logic), or you have a logical system which gives you consistent results and has an explicit boundary of where it can be applied.

So yes, paradoxes exist in logic, but not reality. This is because no logical system can ever map to reality completely, so any that try will always have a paradox. Ideologies attempt rationally construct a political framework that covers all possible things that fall under politics (which can become everything). As such, unless your ideology has a point where it no longer applies, you will never have an ideology without a paradox.