I have never been asked for my research philosophy in an interview. I have only heard this discussed in hardcore anthropology/ethnography circles. My background & experience has been that UX researchers are “Pragmatics.” They “recognize that there are many different ways of interpreting the world and undertaking research, that no single point of view can ever give the entire picture and that there may be multiple realities.” As a result, we tend to use multiple methods to triangulate findings & we pick those methods based on the research question at hand.
For reference, three other research philosophies are:
Did the employer state what his/her/their research philosophy is & why?