On the Gantt chart itself -- or in the columns of the data to the left of the Gantt chart?
For the Gantt chart, I should have given you Format | Text styles.
"The task dates in red obviously mean they are not complete". No, they don't. It could simply mean that the person chose to display text to the left (right, up, down ... you didn't say where those dates are) to be red.
For the columns to the left of the Gantt chart you'd need a VBA macro to conditionally set the font colours.