How where katherine, mary, dorothy, and their coworkers challenged by discrimination? how did they succeeded anyway? hidden figures the movie.

Challenged by segregated facilities. 

The women had to struggle through segregated bathrooms in different buildings and issues with the general distrust of their ability. Many whites believed that blacks carried diseases and you could not touch anything they touched. This is why there were separate bathrooms, coffee, supplies, and work spaces. 

The women proved themselves through their work. Once they proved they could do the work and perform the math, the other workers began to forget about race and focus on the work.