It’s important to clarify that Stanford does not have a music school. It has a music department.
Music schools usually offer a BM and involve auditions. Music departments usually offer BA’s and do not have auditions: it is more of an academic major in many cases, with extracurricular performance (which may involve auditions once on campus). These are sweeping generalizations so yes, check websites.
Stanford’s website says “The Department of Music welcomes all students to participate in the Department’s offerings regardless of their major.”
Furthermore, they invite a supplement (portfolio) but it is optional and does not involve auditions:
The Arts Portfolio in Music
Students with extraordinary talent in music composition, conducting or performance may supplement their Stanford application with an Arts Portfolio. The Arts Portfolio is entirely optional and will be reviewed at the discretion of the Office of Undergraduate Admission and the arts faculty. Students who submit an Arts Portfolio are not required to major in the arts at Stanford. Similarly, students who do not submit an Arts Portfolio may still study or participate in the arts at Stanford.