Background/Objectives: Oral health promotion in early childhood depends strongly on caregivers’ preventive care at home and educational centers. The aim of this study was to investigate socioeconomic, educational, cultural, and oral health factors associated with caregivers’ decisions to decline their children’s participation in school-based oral health promotion programs. Methods: Caregivers who did not authorize their children’s participation in the project were identified through school records and contacted using available information (name, telephone number, and email address). Participants were selected through simple random sampling. Results: Among the 58 caregivers included in the study, the main reasons reported were failure to return the consent form or missing the deadline (36.2%), considering the child too young (19.0%), already receiving private dental care (13.8%), not understanding the consent form (13.8%), not having received the document (10.3%), lack of trust in the professional (3.4%), and other reasons (3.4%). Higher income was significantly associated with higher educational level (p = 0.002), increased toothbrushing frequency (p = 0.007), shorter time since the last dental visit (p < 0.001), and lower levels of embarrassment related to oral health (p < 0.001). Additionally, lower-income caregivers were more likely to seek dental care only in the presence of problems (p = 0.046), while higher-income families were more likely to report private dental care as a reason for non-authorization (p < 0.001). Conclusions: These findings associate socioeconomic and educational inequalities with adverse effects on family oral health among parents, by reducing the frequency of preventive dental examinations and daily oral hygiene practices; and among children, by limiting authorization to participate in school-based oral health promotion programs. This evidence underscores that successful promotion of children’s oral health in educational settings requires addressing social disparities while strengthening caregivers’ knowledge and motivation to support participation.