I know your concern. Sometimes it is really a pain, and just not possible. I always find that I have to "pre-plan" if I want to do things other than watch the parade and it's going to be around parade time. During the afternoon parade, I went on Splash Mountain in Frontierland, then took the train over to Mickey's Toontown in order to give me access to Fantasyland without trying, probably unsuccessfully, to navigate the crowds lining Liberty Square. During the evening parade, I just pick a land not affected, maybe Tomorrowland or Fantasyland, and stay there. You really need to pre-plan , it seems, if you want to get around during the parades.