In what specific areas of southern life did the Plessy decision encourage racial segregation?
Plessy vs. Ferguson gave carte blanche to Southern White supremacists to institutionalize segregation; "separate but equal" was honored more in the breach than in the observance. It's most obvious application was in the education system; blacks and whites were required to attend separate schools with all white teachers in white schools and all Black teachers in Black schools. Blacks were only allowed to enroll in all-Black colleges and universities. Those who applied to public universities--even state supported ones--were turned down on the basis of race. Blacks were not allowed to sit in restaurants frequented by whites; although they could go to the restaurant's back door and order food to go. Movie theaters had separate balconies with separate entrances for Blacks; water fountains and restroom facilities were segregated by race. Public parks and especially swimming pools were normally closed to Blacks. Churches and funeral homes, barber and beauty shops, etc. were all segregated by race.
This writer grew up in the "separate but equal" South, and can offer several personal observations. I well remember as a child taking trips and stopping at service stations with three bathrooms: men, women, and "colored." The third was unfit by use by anyone. The State Fair in my state met in mid-October, followed by a separate Fair the following week for blacks. Neither race attended the other's Fair. On public busses, Blacks were required by law to take the first available seat nearest the back of the bus. If no seat were available except one near a white person, the Black person was required to stand. I also remember attending a tent meeting held by a famous evangelist which had a large area roped off and marked "reserved for colored."
It is important to note that this situation existed so long that it actually became institutionalized through the passage of time. Children were taught at home, at school, and at Sunday School that separation of the races was both natural and proper. This writer began first grade in 1954, the year in which the Supreme Court in Brown vs. Board of Education said that segregation had no place in public education. Even so, no Black students attended my school (I attended the same school, grades 1-12) until my Senior year. I never sat in class with a Black student until my college days. Hence the pervasive effect of the Plessy decision.
I would argue that it is not really proper to say that Plessy encouraged segregation. I would say that Plessy allowed segregation. I do not believe that Southern whites needed to be encouraged to segregate.
However, if you want to argue that Plessy encouraged segregation, there are many specific areas in which this occurred. The most obvious is in public accomodations like the trains around which the case revolved. After Plessy, segregation spread to include things like municipal swimming pools, drinking fountains, and the like. A second area in which segregation became quite common was in schools. In all of these areas, it could easily be argued that the facilities provided for blacks were equal to those provided for whites. This meant that the Plessy doctrine was not violated.
The Plessy decision allowed (or encouraged) segregation in these two broad areas of southern life.