Do admission officers accept letters from religious mentors or extracurricular instructors for homeschooled students?

Yes. Admission officers understand that most homeschooled students don’t have a school counselor. They accept letters of recommendation from any adults who are influential in the students' lives. That said, they're interested in hearing from somebody who understands the applicant’s academic skills, so your child should try to get a letter from one of their course instructors—colleges prefer this not be the parent.

Students who aren’t homeschooled may also be able to submit recommendations from adults who aren't affiliated with their school, but some colleges ask specifically for one letter from a teacher and one from a school counselor. Students may have the option of providing a third letter from any other adult who knows them well.