In an industry dominated by straight men, many developers representing other gender identities and sexual orientations often encounter hateful or discriminatory messages. Such communications pose barriers to participation for women and LGBTQ+ persons. Due to sheer volume, manual inspection of all communications for discriminatory communication is infeasible for a large-scale Free Open-Source Software (FLOSS) community. To address this challenge, this study aims to develop an automated mechanism to identify Sexual orientation and Gender identity Discriminatory (SGID) texts from software developers' communications. On this goal, we trained and evaluated SGID4SE ( Sexual orientation and Gender Identity Discriminatory text identification for (4) Software Engineering texts) as a supervised learning-based SGID detection tool. SGID4SE incorporates six preprocessing steps and ten state-of-the-art algorithms. SGID4SE implements six different strategies to improve the performance of the minority class. We empirically evaluated each strategy and identified an optimum configuration for each algorithm. In our ten-fold cross-validation-based evaluations, a BERT-based model boosts the best performance with 85.9% precision, 80.0% recall, and 82.9% F1-Score for the SGID class. This model achieves 95.7% accuracy and 80.4% Matthews Correlation Coefficient. Our dataset and tool establish a foundation for further research in this direction.