The OP was about scientific inquiry, not about religious commitment or applications of faith. Much research on religion has been done by atheists and agnostics. That doesn't mean it's biased or that it doesn't tell us anything.
Actually, my OP wasn't so much about scientific inquiry. My stance is that scientific inquiry alone isn't all that useful for really understand how humans think about their religious/spiritual lives and how they determine where and how to practice.
I'm interested in the intersection of culture and the individual- how knowledge and practice comes to be social and yet is individually used, manipulated, created, and so forth in individual people. I'm interested in culture as "distributed systems of cognition" (a la Kronenfeld) and how religion may function to open human beings (or not) to something beyond these systems through use of them.
I'm rather skeptical of the functionalist approach, which has often been used in anthro to approach religion. Functionalism is fine, but I think the functional purposes of religion are often emergent rather than embedded in individuals' practice and belief, so it begs the question of what is going on in the individual and how does this translate into social function? That many/most anthropologists are atheist doesn't help, because in some ways that means an unwillingness to be fully open to the usual individual religious experience. It doesn't mean those studies are without merit, but that they are quite limited, as any such inquiry would be.
Overall, though, this is a project that I would do for myself, but with some of the rigor that is expected by my field. Why? Because if you're going to do something, you might as well do it to the best of your ability. Aside from that, the awareness that anthropology has given me of ethics in social research and experimentation (even in my own life) and the methodology to be self-critical of my own thoughts, feelings, and actions assists in a self-reflective approach, which is distinctive from the way most people learn a religion or any culture, for that matter. In many ways, the work would be informed by post-modernism and the phenomenological approach, similar to some studies of landscape by post-modern archaeologists.
That's fine, but scientists are for the most part pretty conservative and are not interested in sampling without knowing what and who they're sampling.
All that said, I am not so interested in questions about this vs that sect in a religion as I am in overarching questions about how the individual experiences communal practice, how community might influence belief and spiritual experience, the question of distributed cognition, intragroup diversity, and so on.
Personally, I am interested, as a mystic-type personality, what I experience in the different religions. That is, how much of religious experience for the individual is guided by their inherent personality and sense of purpose as opposed to the religion itself and group's avowed sense of purpose?
It's a personal journey first. So I'm not as concerned with sampling as I am with finding a group that is open and willing to let me participate. Of course I'd find out what group it is and the history of that sect and so forth, though. I can't imagine not doing that work- I'd be curious for myself.
They're not interested in surprises either. They're intersted in confirming theories. They want replicable results, which calls for carefully designed studies.
I'm interested in surprises. I hope to encounter some. If the world worked the way I thought it did, my work would be quite boring. Nor do I particularly want to confirm theories. I'd rather challenge them.
The post-modern critique in anthropology, while in some ways very unhelpful, did firmly ground us in the sense that our results are unlikely to be replicable, no matter how well we design our studies. We study human beings and groups, and these change over time, often very rapidly. We will never interact with the same exact group or individual twice. Our presence alone makes this impossible.
But that is OK. I am more concerned with honestly representing myself and the subject matter- the inherent limitations of anyone to study this stuff, and yet the value of understanding others within these limitations- than I am with feigning replicability.
With scarce funding resources, a scientist is much more likely to be funded if they have a specific and manageable research question and well defined sample selection method.
That is certainly the case. This type of research would be far too personal and far too fuzzy to get funding from say, NSF. And in order to do that (as I have before) I would have to basically ruin the research design and fall back on the same tired old ways of doing things that have so far been done. Yawn.
Fortunately, this work would be cheap for me to do and so I'd just invest my own money into it.
I actually would not want it funded by anyone, because in some ways, receiving funding demands that you alter your design and become pleasing to the funder. I don't want to be pleasing to someone else. I want to be honest to the experience itself.
In research, replicability is always an issue. Other researchers would wants to know where the sample came from in order to improve their chances of repeating or extending your findings. If the sample, characteristics are relevant to other variables of interest, it may be impossible for anyone to replicate in any other sample. Soon no one would cite your research anymore and that would be that.
I see this as a big problem in social science. If we are honest with ourselves, very little of anything of interest is replicable. People are not consistent in their behavior, and the personality of the researcher matters a great deal in any study in which the researcher does anything with participants. Even just interviewing people will have different results depending on the researcher- both their external qualities (gender, ethnicity, etc.) and their personality and intelligence. We should be honest and get over the fact that you can't study people the way you study bacteria.
In this type of journey/project, my own goals, views, and personality would matter a great deal. In fact, that is partly what I am critiqueing- that if you approach religious experience as an atheistic bystander, you simply aren't going to get as much out of it (or as much information out of practitioners!) as you would if you approach it as an open-minded seeker. In turn, my experience as such would differ from a "real" convert who intends to only be in that one religion for life. The way I see it, it is better that we are honest about these differences than to cover them up with feigned replicability.
As for people citing my research, to be bluntly honest, I could care less if I am entirely forgotten in my discipline. I got into anthropology in order to understand people better with the hope of spreading peace, understanding, and love of others. And with the practical hope that understanding how people think individually and in groups, how they make decisions, and how they generate a sense of social ethical order might make it easier to mediate conflict, foster inter-cultural understanding, and illuminate ways to generate sustainability and alleviate suffering. I'm a practical idealist.
I'm far more interested in publishing this project (if I did it) as a book for the public, or a PBS special, or a Nat Geo thing. I'd hope to spread inter-religious understanding through it, and some sort of joy and humor. I'm far less interested in what it would give to anthropology because, quite frankly, it's just not my primary concern. I do other research on cognition in much more tightly controlled environments that contribute to anthropological theory and method. It would be likely that the journey/project would give me some ideas and venues for cognitive research, but this would not be to understand religion, but rather to understand the structure and use of individual thought and cultural knowledge.
So, my long-winded way of saying- this project is informed by anthropology, but would not be done with the purpose of contributing to anthropology except as a critique. Publications arising from it would be for the popular press, not the academic ones. I find writing for academic purposes to be rather a dry and boring exercise anyway. As one of my students said:
"Why are anthropologists' stories so interesting, but their books are so boring?"
Why, indeed?