Well, one way to answer the question is to take a look at the requirements for a few top programs in anthropology.
McGill’s MA in sociocultural anthropology:
Admission to the MA program is open competitively to students holding an Honours or Major BA in Anthropology, although special provisions are made in the MA program in Medical Anthropology for students with a joint expertise in Health Sciences and Anthropology. Outstanding candidates with Bachelor’s degrees in other disciplines but with substantial background related to Anthropology are sometimes admitted on the condition that they complete a specified number of additional courses in Anthropology.
University of Toronto:
Applicants to the MA and MSc programs are expected to hold an appropriate Bachelor’s degree, with a final year average of at least B+ or its equivalent from a recognized university. Normally, students must have at least five full-year Anthropology courses (or equivalent) with a minimum average of B+ to allow them to specialize in their proposed areas of study. However, the department also welcomes applications from students with competence in related fields, in line with our interest in innovative cross-field and cross-disciplinary work. Students who have done coursework in related fields which they would like the admissions committee to consider should attach a separate sheet as a last page to the research statement, listing these courses and explaining the relevance to the proposed program of study in anthropology.
University of British Columbia:
Applicants must hold a four-year bachelor’s degree with a major, honours or concentration in anthropology or the equivalent…In addition, applicants to the MA program must have completed at least 12 credits in senior anthropology courses with a minimum average of A -…Outstanding candidates with undergraduate degrees in other disciplines but with substantial background related to anthropology, or who are missing one or more of our admission requirements, are occasionally admitted on the condition that they complete a number of additional courses in anthropology.
Columbia’s MA in sociocultural anthropology:
- We prefer to admit students who have some background in anthropology, but an undergraduate degree in anthropology is not required.*
Hunter College:
Applicants thus often come from unusually cosmopolitan backgrounds, and our admissions policy is adjusted to a high degree of variability in level of training and prior background in anthropology. Our admissions system-- administered by the College’s Graduate Admissions Office-- is two-tiered: highly qualified applicants with strong backgrounds may be accepted system directly into the Master’s Program as “matriculated” students. Highly motivated applicants who have little previous background in anthropology are occasionally admitted with “non-matriculated” status. After completing one to three courses with grades of “B” or higher, non-matriculated students may apply to the Master’s Program. Admission with non-matriculated status is in no way a guarantee of admission to the Master’s Program.
It’s much harder to find these kinds of statements on American universities’ websites, for some reason - I checked out a couple of other big anthropology departments that offer MAs (Stanford, Berkeley) and they had no such information. A lot of anthropology departments in the U.S. also don’t offer a terminal MA.
So it appears that it is not negligible in the long run: if you want an MA and later a PhD in anthropology, your best bet is to change your major to an anthro-related major.
However, I’m checking out LB’s classes in the society, culture, and environment major and they don’t look directly comparable to a major in anthropology. There are a lot of classes with interesting titles, but no classes on physical anthropology, ethnography, research methods, or anthropological theory. Those are the classes that these programs expect you to take in an anthropology major (UBC says it explicitly on their website).
So staying in your criminology major won’t hurt you if your only other option is the SCE major. If you had the option of an anthropology major, I’d say change to that, but since you don’t, it probably doesn’t matter in the long run. Do see if you can take some of the culture-related classes, though, particularly if they are taught by anthropologists and maybe include some theory.