The #MeToo movement has catalyzed widespread public discourse surrounding sexual harassment and assault, empowering survivors to share their stories and holding perpetrators accountable. While the movement has had a substantial and largely positive influence, this study aims to examine the potential negative consequences in the form of increased hostility against women and men on the social media platform Twitter. By analyzing tweets shared between October 2017 and January 2020 by more than 47.1k individuals who had either disclosed their own sexual abuse experiences on Twitter or engaged in discussions about the movement, we identify the overall increase in gender-based hostility towards both women and men since the start of the movement. We also monitor 16 pivotal real-life events that shaped the #MeToo movement to identify how these events may have amplified negative discussions targeting the opposite gender on Twitter. Furthermore, we conduct a thematic content analysis of a subset of gender-based hostile tweets, which helps us identify recurring themes and underlying motivations driving the expressions of anger and resentment from both men and women concerning the #MeToo movement. This study highlights the need for a nuanced understanding of the impact of social movements on online discourse and underscores the importance of addressing gender-based hostility in the digital sphere.