Social media platforms employ inferential analytics methods to guess user preferences and may include sensitive attributes such as race, gender, sexual orientation, and political opinions. These methods are often opaque, but they can have significant effects such as predicting behaviors for marketing purposes, influencing behavior for profit, serving attention economics, and reinforcing existing biases such as gender stereotyping. Although two international human rights treaties include express obligations relating to harmful and wrongful stereotyping, these stereotypes persist both online and offline, and platforms often appear to fail to understand that gender is not merely a binary of being a 'man' or a 'woman,' but is socially constructed. Our study investigates the impact of algorithmic bias on inadvertent privacy violations and the reinforcement of social prejudices of gender and sexuality through a multidisciplinary perspective including legal, computer science, and queer media viewpoints. We conducted an online survey to understand whether and how Twitter inferred the gender of users. Beyond Twitter's binary understanding of gender and the inevitability of the gender inference as part of Twitter's personalization trade-off, the results show that Twitter misgendered users in nearly 20% of the cases (N=109). Although not apparently correlated, only 8% of the straight male respondents were misgendered, compared to 25% of gay men and 16% of straight women. Our contribution shows how the lack of attention to gender in gender classifiers exacerbates existing biases and affects marginalized communities. With our paper, we hope to promote the online account for privacy, diversity, and inclusion and advocate for the freedom of identity that everyone should have online and offline.