Although intention to quit has been extensively examined for heterosexual teachers, there are almost no related findings for teachers who belong to the LGBTQ+ community (lesbians, gays, bisexuals, transgenders, queers, questioning individuals or others with non-cisgender/non-straight identities). Also, the role of perceived school and social contributors to their intention to quit is significantly under-explored for both teacher subgroups. Consequently, the present study comparatively investigated intention to quit between heterosexual and LGBTQ+ teachers. Additionally, applying the Job Demands-Resources model, the contributing role of perceived school climate and social support was co-examined for each teacher subgroup. Overall, 342 elementary school teachers (n = 181 heterosexual [61% women], n = 161 LGBTQ+ [66% women]), who were employed in Greek public schools from almost all Regional Education Directorates, completed online self-report scales related to the variables involved (intention to quit, perceived school climate, perceived social support). The results showed that LGBTQ+ teachers' intention to quit was above average, and it was expressed to a greater extent, compared to heterosexual teachers. Furthermore, regarding heterosexual teachers, it was found that, primarily, student relations and school resources (dimensions of perceived school climate) and, secondarily, family support (dimension of perceived social support) were negatively contributed to their intention to quit. As far as LGBTQ+ teachers, primarily, collaboration and decision making (dimensions of perceived school climate) and, secondarily, all the sources of perceived social support (family, friends, significant others) were negatively contributed to their intention to quit. The findings imply the necessity to intensify psycho-educational actions aimed at strengthening differentiated underlying psychological mechanisms inside (positive school climate) and outside school (supportive social environment) for heterosexual and LGBTQ+ teachers. In this way, both teacher subgroups' future intention to quit may be weakened.