AThe Director's Cut of Remember the Titans is to be considered rather positively. Beside numerous small extensions and just as many edits, especially three pretty long new plot scenes have been reimplemented into the movie, of which especially the final and longest scene must be emphasized. It concludes a plot line which couldn't be considered incomplete in the Theatrical Version, but still enhances the movie immensely and depicts a small highlight. A detailed comparison between both versions with pictures can be found here.
AYes, however, don't be fooled into thinking what you see on the screen actually happened. The movie is very heavily fictionalized and Hollywoodized, and the facts are often dramatically different from the movie. Alexandria, VA, shown as a small rural town in the movie, is actually a bustling suburb of Washington DC. T.C. Williams High School had been integrated since 1963. Rather than integration being responsible for the winning season, it was consolidation with two other schools that gave them a larger talent pool to choose from: they had the best athletes from three schools. By 1971, all the teams in their league were integrated, and much of the racial tension depicted in the movie was fiction, invented for dramatic effect. The dramatic midnight run and the memorable, dramatic speech about Gettysburg are complete fabrications that never occurred in real life. The Titans also faced little challenge in that season; the game in the movie, in which they needed to make an exciting last-minute touchdown to win, is also complete fiction. In that game, the Titans had an absurdly easy victory, trouncing their opponents 27-0, and proceeded to walk all over other teams to a championship season.