I went through the red cross in MA. They used to be able to wear street clothes during class but they changed the whole policy. You have to wear scrubs during class and clinicials. Plus, they changed the scrub color (after i already bought white ones).
Just ask your school. Everyone here, even in the high school CNA classes, wears scrubs during class to put you in the mood of being in health care. If they require scrubs, often they will have a specific color in mind based on the facilities that you'll do clinicals in.
I am currently in a class now and we are required to wear scrubs at all times even in class. We can were any color, pattern or style but they do require us to wear them. When we do our clinicals next week they said that we can wear any scrubs that we want as long as we wear student ids to stand out. Just ask and if they tell you to buy them I would suggest a second hand store like goodwill they are only a couple bucks because most places when they hire make you wear a uniform.