These professors were accused of being communist sympathizers. This resulted in their dismissal from the University of Washington. One of the biggest reasons why this was a big deal was due to the beginning of the Cold War and the start of the second Red Scare.
After World War II, the US and Soviet Union emerged as global superpower. As communism spread throughout Eastern Europe, US citizens were scared that this system would spread to the US. In order to prevent this from happening, institutions all over the country took action against supposed communists, including firing them from their jobs.