I personally think it’s unrealistic to expect children and teenagers to never listen to pop music. Unless they are homeschooled and only exposed to other children and teenagers with the same upbringing, they will hear pop music, and most of them will come to like it. Most of them will develop crushes on various pop artists and this is perfectly normal and healthy, as it prepares a child to love a real man or woman someday.
IMO, the child or teenager who is most likely to like all kinds of music is the child or teenager who is actually a musician themselves.
I play piano, and I work with a lot of the most artistic, musical children and teenagers in our city. Several of them are professional singers/actors with various theaters in the Chicago area. These kids are quite knowledgeable about music from all genres. Many play piano or another instruments, and many are fans of opera, classical music, sacred music (many earn money singing in various churches and at weddings and funerals), etc.
But they also like pop music and other modern genres, including rock, R & B, jazz, rap, hip hop, and even the rauchier stuff. Many like various ethnic music genres, especially Indian and African. Some like CW, especially crossover artists like Taylor Swift. Only a few like hardcore country (Clint Black, Alan Jackson, Randy Travis, etc.) Only a few (very few) like CCM (Contemporary Christian Music).
I think it’s very possible for kids and grownups to like or at least appreciate all genres of music because I see it all the time with artistic kids.
So my suggestion to the OP is that if you want your chld to appreciate all kinds of music, get her into piano lessons, or lessons on another instruments that requires exposure to a classical repertoire. And make sure she is involved with musical theater, either as a performer or a techie.