Do you have a professional degree unrelated to your undergrad?

Kind of an odd question. What constitutes a professional degree? Med and law, right?

Yep...BA in Psychology; MBA in Accounting

A "professional" is a person in engaged in a service oriented occupation in which the free exchange of information is so overwhelmingly important with individuals relying upon those services that communication shared to the "professional" is deemed confidential and secret. That said, there are only three (3) legally recognized professionals: (1) doctors, (2) lawyers, and (3) clegypersons. Communication between a physician and a patient is very important for the doctor to render competent medical care and accordingly a "privilege" is granted and doctor is ethically obligated not to disclose information gained from patient seeking medical care. Similarly, an attorney needs as much information as possible from a client and only in special circumstances may an attorney divulge information gained in the course of representing a client. Finally, priests, pastors. rabbis, etc. may hear deeply personal and intimate accounts from parishioners in the course of "going to confession" or private individual counselling and so law has long recognized the "Church Confession " privilege. Admittedly, there has been some argument for courts and legislatures to adopt an "Accountant Privilege," based up privacy of financial record, but acceptance of this concept is still quite limited.

As to the work carried on by people holding a "Master of Public Administration," "Master of Library Science," or "Master of Engineering" degree, there is little expectation for someone to come see: the "chief building planner" overseeing street construction and repair, the "reference librarian" down at public library, and/or "electrical engineer" at power company and share any "personal" and/or "confidential" information with any of them. In fact, under the Freedom of Information Act the city building planner and engineer are obligated to make records available for public inspection when requested.

All of that said, a "professional degree" is one which permits the person upon earning it to enter into the professional work field for which the particular degree is a prerequisite after complying with all other certification criteria. For, lawyers, and there are a lot of us around here, that would be getting approved as having "outstanding moral character" by ethic panel and passing the bar examination. Accordingly, the only "professional degrees" include:
(1) the medical degrees (e.g., M.D., D.D.S., D.O., etc.),
(2) the J.D. earned in law school [Interesting to note that it was not all that many years ago (as late as the 1950) that law schools were still awarding graduates an LL.B. degree and they changed the letters because they had decided to only admit students who had first earned a four-year bachelor's degree and it seemed stupid to be giving their graduates another bachelor's degree!], and
(3) the M.Div. earned at a theological seminary [Just as with law schools awarded graduates an LL.B. degree, clergymen back a few years ago earned a B.Div., but after they decided to only admit students who had first earned a four-year bachelor's degree they changed the name of the degree!].
All three drgrees are basically unrelated to prior college work with the exception of seminaries, which requires applicants to have taken college courses in Greek language, and those who have not had such a course (i.e., many students) must add it as a (remedial or "make-up") class to take in seminary, but won't be counted toward hours needed for graduation!

a lot of colleges don't have equivalent undergraduate programs. until recently, Penn was the only ivy with a real undergraduate business program.

Very few schools have undergraduate programs in Library Science.
The MLS is the entry level degree for the profession.