Understanding ideological conflict has been a topic of interest in CSCW, for example in Value Sensitive Design research. More specifically, understanding ideological conflict is important for studying social media platforms like Twitter, which provide the ability for people to freely express their thoughts and opinions on contentious political events. In this work, we examine Twitter data to understand the moral, affective, and cognitive differences in language use between two opposing sides of the political debate over immigration related issues in the United States in the year since the 2016 presidential election. In total, we analyzed and compared the language of 45,045 pro-immigration tweets and 11,213 anti-immigration tweets spread across this period. Based on Moral Foundations Theory used to understand ideological conflict, we found pro-immigration tweets to contain more language associated with moral foundations of harm, fairness, and loyalty. Anti-immigration tweets contained more language associated with moral foundations of authority, more words associated with cognitive rigidity and more 3rd person pronouns and negative emotion. We discuss the implications of our research for political communication over social media, and for incorporating Moral Foundations Theory into other CSCW research. We discuss the potential application of this theory for Value Sensitive Design research.