Another theme is the power of music. Their shared passion for music can bring them together in various ways. It could be that they use music to communicate when words fail, or that they find solace in creating music together in the midst of the chaos of the opera house.
One common theme is redemption. The Phantom, often seen as a tragic figure, may seek redemption through his relationship with Christine. He might change his ways and learn to love in a more positive and selfless manner.
Friendship is also a major theme. Even though there is often a romantic undertone in their relationship in the original story, in many fanfictions, they form a strong friendship. Christine might be the first person to truly see the Phantom as a person, not just a monster, and this friendship can grow and develop in different and interesting ways.