"research shows that people are more likely to stereotype others or give in to their prejudices when "

The answer is their own self-esteem is threatened
For example, let's say there your rival (who is a taleted female engineer) somehow earn herslef a promotion that you're also after.
In this case, your tendency to display stereotype will higher compared to your usual days. You are very likely to think 'the company only give her the promotion because our male boss favor her' or other form of stereotypes.