What are two social agents that might potentially contradict each other?

Because agents exist in every aspect of society, any two social agents might potentially contradict each other. A social agent can be a people, a nation, even an ideology.
At the abstract level, religion and government can be contradictory agents. In the US, our constitution mandates that there is no official religion, so church is not part of state. Many other countries, however, do have official religions, so the contradiction is not conceptual.
Looking at the realm of the nation, different collectivities often contradict the nation. In the United States, for example, the Founding Fathers decreed that the nation had "liberty for all," but within the new country, slavery remained legal for almost another century. In that regard, the social agent constituted by enslaved persons contradicted the nation.
When the issue of slavery was heightened beyond contradiction to all-out war in the 1860s, the social agent of the Confederacy contradicted that of the United States, as it considered itself a separate nation. In this case, the contradiction was played out in military conflict.
Looking internationally, we can see political economy as an area where social agents contradict each other. In Marxist theory, the owner and the worker are fundamentally at odds, as the owner is always trying to maximize the worker's labor for the least amount of money (exploitation), while the worker aims to gain the maximum amount of earnings, and sometimes benefits, goods, or services. Negotiation over the terms of a contract carried out by a union, or a strike for better conditions, are places the contradictions might be publicly expressed.