Social Determinants and Equity in Health Insurance Access: An Empirical Study Based on CGSS 2021 Data

China’s medical insurance system has reached near-universal coverage, yet disparities in access and quality persist. This study investigates how social structural factors shape coverage and quality in the Chinese context. Using 2021 China General Social Survey data (n = 8148), binary logistic regression was applied to basic and commercial insurance participation, and multiple linear regression assessed a composite quality indicator. Predictors included education, income, gender, household registration (hukou), and age. Basic insurance coverage was 94.3%, with education (OR = 1.180, p = 0.003) and income (OR = 1.281, p < 0.001) as positive predictors; gender and hukou were nonsignificant. Commercial insurance coverage was 14.0% and positively associated with education (OR = 1.357), income (OR = 1.276), and urban hukou (OR = 1.180), but negatively with female gender (OR = 0.800) and age (OR = 0.979; all p < 0.01). For quality, education (B = 0.042) and income (B = 0.040) had the strongest positive effects, while gender (B = −0.032) and age (B = −0.002) were negative; urban hukou had a small positive effect (B = 0.014). Socioeconomic status—especially education and income—consistently predicts higher coverage and quality. Urban-rural differences are minimal for basic coverage but remain for commercial insurance and quality. Policies should target low-SES groups, women, and older adults through premium subsidies, product customization, and awareness campaigns to advance equity in China’s health insurance system.