Seeing as the term "allopathic medicine" refers to western, or modern, medical practices it seems logical that those practitioners should obtain a medical degree. Practicing medicine without a license is a crime. Also, prescribing pharmaceuticals without a degree and/or license to indicate that one is well educated in the use of those chemically based medications would also be criminal. So, yes, practitioners of allopathic medicine should definitely have degrees.
The definition of allopathic describes the conventional practice of medicine in the United States currently. Although it is not perfect, modern medicine and surgery has cured and saved many millions of people already. Preventable deaths are still occurring, caused by both germs and cancers, so it is reasonable to continue training and granting degrees to the people who are combating this problem.
Allopathic, as the proponents of homeopathic medicine call it, is not some weird sub branch of medicine, but is the real, actual science that has been developed over hundreds of years using the scientific method in order to test their theories and figure out how the human body works and operates.
Degrees should be given for allopathic medicine practitioners simply because there should be a minimum set of standards for this kind of medical art. Allopathic medicine may not be mainstream, but enough people know about it that some governing board should be able to license allopathic doctors. There are plenty of alternative medical treatments out there, and allopathy is one of them.
No, I do not think that degrees should be given for allopathic medicine practitioners, because there is nothing about their work that requires a formal degree. Also handing out medical degrees to allopathic practitioners would confuse the public as to what type of doctor a person is and what they can do for their health.