For the purpose of acceptance into a program, no, major doesn't seem to matter. GPA and prerequisites seem to carry more weight.
In a broader sense, does major "matter"? Absolutely. Exercise science and kines majors definitely had a leg up our first semester. Bio and chem majors had an easier time with the basics in pharmacology. My education background made topics on learning styles and related topics easy. Neuroscience majors will undoubtedly benefit from their prior knowledge. The background you have, whatever it may be, will "matter" and be put to use somewhere in class or clinic.