The American Physical Society calls on its members to improve the diversity of physics by supporting an inclusive culture that encourages women and people of color to become physicists. Becoming a physicist demands a set of beliefs about what it means to learn and do physics. Rather than physics courses and degree programs supporting students in developing these beliefs, evidence shows that physics education filters out students without sufficient beliefs. To better understand the role of beliefs in the lack of diversity in physics, we investigated the intersectional nature of race/racism and gender/sexism in inequities in student beliefs towards learning and doing physics using a critical quantitative intersectionality framework. The analyses used hierarchical linear models to examine students' beliefs as measured by the Colorado learning attitudes about science survey. The data came from the LASSO database and included 1248 students in 29 calculus-based mechanics courses. Like prior studies, we found that beliefs either did not change or slightly decreased for most groups. Results identified large differences across intersecting race and gender groups. White students, particularly White men, tended to have more expert-like beliefs than any other group of students. Physics instruction must address these educational debts to move toward an inclusive culture supportive of diverse students and professionals.