Preheat oven to 325°F. Melt margarine in a large nonstick skillet. Add celery and onion. Sauté until vegetables are very tender, about 10 minutes. Stir in thyme, sage, salt (optional), and pepper. Set aside.
Meanwhile, place bread slices on a baking sheet and lightly toast on both sides, about 10 minutes per side (or you can use the toaster). Break bread into bite-size pieces. Mix in vegetable mixture and parsley. (At this point, stuffing can be made one day ahead, placed in a self-sealing container, and refrigerated.)
In a medium saucepan, heat broth to a simmer. Place dressing mixture in a large mixing bowl. Add hot broth and stir until bread is evenly moistened, starting with 2½ cups broth and adding additional broth to reach desired consistency. Transfer mixture to a shallow baking dish. Cover with foil and bake for 30 minutes. Uncover and continue to bake until lightly browned, another 15 to 20 minutes.