Background/Objectives: The aim is to assess public stigma related to people with mental health problems and to observe the influence of sociodemographic factors on it. Methods: This observational, descriptive, and cross-sectional study was conducted with a sample of 404 participants who completed a self-administered online questionnaire that included sociodemographic variables and the Community Attitudes towards Mental Illness Scale (CAMI-S, Spanish version). Non-parametric tests, multiple linear regression, and statistical power analyses were applied. Results: The mean CAMI-S total score was 84.89 (SD = 11.122), indicating a generally positive attitude towards community integration. Statistically significant associations (p-value ≤ 0.05) were found between CAMI-S scores and variables such as gender, age, place of residence, educational level, mental health disorder, and close contact with someone with mental health disorders. The regression model revealed four significant predictors of lower stigma: identifying as female (β = 2.523; p = 0.037), having a medium or higher educational level (β = 5.061; p = 0.002), experiencing a mental health diagnosis (β = 4.535; p = 0.014), and a close contact (β = 4.183; p < 0.001). Conclusions: These findings underscore the need for targeted anti-stigma strategies and reinforce the role of nursing in promoting mental health inclusion.