Access to dual-enrollment courses, which allow high school students to earn college credit, is stratified by race/ethnicity, class, and geography. States and colleges have begun using "multiple measures" of readiness, including "non-cognitive" measures of student preparedness, in lieu of strict reliance on test scores in an attempt to expand and equalize access. This practice was accelerated by COVID-19 due to disruptions in standardized testing. However, limited research has examined how "non-cognitive" beliefs shape students' experiences and outcomes in dual-enrollment courses. We study a large dual-enrollment program created by a university in the Southwest to examine these patterns. We find that mathematics self-efficacy and educational expectations predict performance in dual-enrollment courses, even when controlling for students' academic preparedness, while factors such as high school belonging, college belonging, and self-efficacy in other academic domains are unrelated to academic performance. However, we find that students of color and first-generation students have lower self-efficacy and educational expectations before enrolling in dual-enrollment courses, in addition to having lower levels of academic preparation. These findings suggest that using non-cognitive measures to determine student eligibility for dual-enrollment courses could exacerbate, rather than ameliorate, inequitable patterns of participation. Students from historically marginalized populations may benefit from social-psychological as well as academic supports in order to receive maximum benefits from early postsecondary opportunities such as dual-enrollment. Our findings have implications for how states and dual-enrollment programs determine eligibility for dual-enrollment as well as how dual-enrollment programs should be designed and delivered in order to promote equity in college preparedness.