<p>Many mathematics education scholars agree that university mathematics needs to do a better job of supporting equitable classroom practices. While prior work has described the beliefs of university instructors who are relatively unsupportive of equitable instructional practices, there is relatively little work exploring the perceived barriers of instructors who are amenable towards these practices. In this interview study, seven mathematics graduate teaching assistants described their perceived barriers to implementing equitable practices, in the form of culturally relevant pedagogical practices, in their undergraduate mathematics classrooms. Ultimately, even if an instructor was receptive towards the goals of a recommendation, they were sometimes unwilling to implement it if they felt it conflicted with other obligations they held. The graduate teaching assistants described three types of obligations that restricted their ability to implement various recommendations in service of equitable instruction: institutional obligations, an obligation to safeguard students’ wellbeing, and an obligation to respect student agency and feedback. These perceived tensions highlight the role of broader institutional and societal barriers and how they may constrain university instructors even if they are amenable towards equitable practices.</p>