Academic regalia varies throughout the West, but it primarily consists of a robe, a cap, and a hood. Differences within systems of regalia reflect the type of highest degree earned by the person, the subject matter of that degree, and the school at which that degree was earned. Additional adornments may reflect special affiliations or honors earned by the recipient.
In my own limited experience, the most significant indicators are the found in the hood, which is short for a master's degree or long for a doctorate. The outer color represents the discipline, such as orange for engineering or pink for music. The inner two colors are the school colors of the university which granted that degree.
So Theresa wonders which disciplinary color Dumbledore would wear as a professor of magic. She proposes scarlet for theology. I think that one could argue for the dark blue of philosophy. Alternatively, Dumbledore might actually have his doctorate (if any) in higher education administration, as many school administrators do. In this case, his hood would be light blue.
Image: Warner Bros., Wikimedia Commons, respectively