From the Princeton website:
SAT Subject Tests. We recommend, but do not require, the submission of two SAT Subject Tests, which often assist us in the evaluation process. We have no preference for the specific SAT Subject Tests applicants might choose to take. However, if you apply for the B.S.E. degree, we recommend that you take mathematics (Level I or II) and either physics of chemistry. If you decide to submit Subject Tests, early action applicants should take them by the November test date, and regular decision applicants should take them by the January test date.
https://admission.princeton.edu/applyingforadmission/application-checklist
Note that SAT Subject Test scores are components of the Academic Index, so if a recruited athlete is not already planning to take them , coach would probably insist