Did you also apply for studentships in "tribal communities and identity"? And is "survey data analysis" within the Sociology department?
Your PhD doesn't ultimately limit what you can research afterwards (within reason) but there has to be some sort of link that can take you from one area to another. Since Sociology is a particularly multi-disciplinary subject, I don't think it's an implausible route to your area of academia. It's not uncommon for those in very niche, under-funded areas struggling to get a studentship to apply for a more general PhD, but your success in becoming a lecturer depends on how many post-docs there are available through which you could make the transition. Have you taken a look at what the lecturers in your research area are publishing? Is there much cross-over with your particular interest in Sociology?
As for actually doing the PhD, it will certainly be more of a challenge if you are not strongly interested in your work, if only for the reason that the main obstacle in completing a PhD is the constant self-motivation required. It's three years of battling to be productive (and creative) through self-direction, which is notably more difficult than an office job you dislike in which your work is delegated to you. However, since you clearly have some level of interest in the area and "naturally enjoy data analysis", it seems very much doable. The more pressing concern appears to be whether you can direct your career towards the area of research you prefer, and how long this would take. It might be the case that you would be doing pure data analysis for longer than the three years. I would do some extensive research into the professors of your field and look for similarities with your own plans.