When training teen singers, I don’t encourage a specialization in repertoire. If they are going to audition for music degrees, they often have to prepare repertoire from classical, musical theatre, and popular styles. Having a generally tension-free voice with two octaves of usable range and a clear connection to the text and a well-prepared audition will usually get them into a suitable program. I have to remember their goals and give them a foundation from which they can go deeper into something specific later.
Singing multiple styles has some specific benefits to young singers. It can get them to explore different flavors of expression, helping them to find out what they connect to as artists. It can provide them with more performance opportunities than specialization would. It can help them to discover strengths, both artistically and technically, which may or may not be the same as what they love the most.
If they are doing regular workouts of effective vocal exercises that are designed to keep the voice flexible, strong, and coordinated, singing multiple styles should not be a problem. The workout needs to cover the domains of agility, flexibility, range, register transition, dynamic control, and a clear understanding of the function and behavior of vowels. Regular, consistent training of this sort will keep them safe.
I occasionally have a student who wants to major in classical voice specifically, but I still encourage them to sing a few things beyond the boundaries of “classical”, such as old standards, musical theatre, or various folk traditions. Asking such a student to stretch a little here and there usually helps them in the long run.