The literature regarding vaccine hesitancy is limited to specific vaccines rather than general vaccine hesitancy. No studies have examined the relationship of general vaccine hesitancy to healthcare access and experiences of racial discrimination. This study fills gaps by examining: (1) socio-demographic factors; (2) associations between healthcare access; and (3) experiences with racial discrimination and general vaccine hesitancy. Survey data were obtained from 2022 US adults from 7 September to 3 October 2021. Racial and ethnic minority populations were oversampled. Age, gender, race, and education were predictors of vaccine hesitancy. Asian respondents had less than two-thirds the odds of being vaccine hesitant. Healthcare access was associated with vaccine hesitancy. Not having health insurance coverage, not having a primary care provider, and not seeing a provider for a routine check-up in the past two years were associated with higher vaccine hesitancy. For every one-point increase in racial discrimination score (0–45), the odds of being more vaccine hesitant increased by a factor of 1.03. The findings demonstrate that policy, systems, and environmental factors are critical to addressing vaccine hesitancy. Given the associations between vaccine hesitancy and racial discrimination and healthcare access, more attention should be given to inequities in the healthcare systems in order to address vaccine hesitancy.