Psychological stress detection is an important task for mental healthcare research, but there has been little prior work investigating the effectiveness of psychological stress models on minority individuals, who are especially vulnerable to poor mental health outcomes. In this work, we use the related task of minority stress detection to evaluate the ability of psychological stress models to understand the language of sexual and gender minorities. We find that traditional psychological stress models underperform on minority stress detection, and we propose using emotion-infused models to reduce that performance disparity. We further demonstrate that multi-task psychological stress models outperform the current state-of-the-art for minority stress detection without directly training on minority stress data. We provide explanatory analysis showing that minority communities have different distributions of emotions than the general population and that emotion-infused models improve the performance of stress models on underrepresented groups because of their effectiveness in low-data environments, and we propose that integrating emotions may benefit underrepresented groups in other mental health detection tasks.