Transfer status does not matter. Major status might, but this depends on your university.
At my first university, which was a large state school, anyone could enroll in the pre-requisite courses regardless of major. What mattered was if you wanted to take any upper-division science courses like genetics - you had to declare yourself a biology major. At my second university, anyone could enroll in the pre-reqs, and anyone could enroll in upper-division science courses, with the exception of anatomy and physiology, which were reserved for "health science" and nursing majors.