After I thought about the relationship of genealogy as a discipline to either art or science, I decided to look online and see what was there. To my surprise (not really) it turns out that the subject is not widely discussed. I did find one Blog post on the subject called "Genealogy is an Art" from the year 2000. Right out of the chute, I must say that I disagree with this Blogger's assessment. Although genealogy, in my opinion, is not an art, it is only partially a science. What is certain is that genealogy can only overcome its inherent limitations as a discipline to the extent that its methodology becomes scientific.
One of the main challenges of genealogy as a serious pursuit originates in the failure of many, perhaps most, of its adherents to follow any sort of rigorous methodology. Genealogy should be considered a branch of History (with a capital "H"). But it is notable that there is only the most tenuous connection between the mainstream of historical research and genealogy as a discipline. There are a mere handful of schools and only one university that award degrees in genealogy. There are two four-year programs, one at the Heritage Genealogy College, a privately operated school in Salt Lake City, Utah and Brigham Young University, in Provo, Utah. Other schools offer associate degrees and class credit.
I do not believe that universities have a monopoly on either learning or teaching, but the lack of association of genealogy with established university departments, indicates that genealogy is certainly not an accepted academic discipline. Why is that the case? Part of the explanation lies in the historical context. In years past, genealogists (or those claiming to be) were self appointed and unregulated. Unlike some disciplines, such as medicine and law, that started out with no academic requirements and now have widespread academic endorsement, genealogists never organized and regularized their discipline.
As an example, in the 1800s and before in the United States, a person did not "go to law school" to become an attorney. If a person wanted to practice law, they simply bought some law books and started to read and perhaps associated with an already established attorney. Ultimately, they could practice law by being "admitted" to the practice by the courts. Although in England during the same time period, the practice was more structured, there were no law schools. The first law school in America was the Litchfield Law School in Litchfield, Connecticut established in 1772. but until late in the 1800s law school attendance was very rare. There are still states where a law degree from an accredited law school is not a requirement to practice law and students can get a qualifying degree from an online correspondence school.
Genealogy, unlike law, never became an organized profession. Even today, there are no government imposed qualifications for becoming a professional genealogist even though most states regulate every profession from dog grooming to hair styling. Despite the efforts of the various genealogical boards and other professional institutions, very few of the practitioners of genealogy obtain any kind of professional credential and none is required to become a "professional" genealogist.
The absence of genealogy as either an academic discipline or as a regulated profession is obvious from the advertising that goes along with the sale of genealogically related products that advertise how easy they make genealogy. Also, the constant emphasis on how many people can "do" genealogy is exactly contrary to ever having the subject accepted by either academia or as a profession.
Is this a problem? Well, many of the issues with sloppy and incompletely sourced family trees comes from the inclusive nature of the discipline. We can't have it both ways. Either genealogy is a pastime or it is a profession. If it tries to be both then it will always be part science and part hobby.