This is all written without my moderator hat on, mostly because none of my thoughts on the matter have affected my way of moderation.
Normally, I don't care what an answerer believes in. I really don't. What I do care about is whether or not s/he knows his/her stuff. If that means that s/he must be intimately familiar with the culture at hand, then being a believer can become important.
The religious Stack Exchange sites have, of course, all discussed the practice of citing sources, what kinds of sources should, be used, and related topics, with varying results. A few touched on the idea of expert answers, so I think I'll summarize the ideas they came up with1:
Buddhism: The general consensus, as given in What about providing sources?, seems to be that answers should not have to require sources, because expert answers are more important. Andrei Volkov's answer touches on the fact that people with no experience whatsoever in Buddhism could simply come up will well-referenced answers that wouldn't be written by experts. He brought up a point similar to yours, and yet different still:
The basic question is: do we trust our experts, and do we believe that the reputation-based open community will correctly identify experts as such -- or do we presume that only published authors can be trusted?
The main relevant point here is that answerers should be experts, and, in the case of Mythology, we need to know that they are experts.
Christianity: What is "mainstream" Christianity? is the most important post on the site in this regard, as far as I can see. Quoting the main, community wiki answer,
What we are trying to do is differentiate between the belief of an individual (which is not a scholarly pursuit) from those historical groups of Christianity which are the subject of of scholarly study.
The important thing I got out of this is that it is important to show that what you write is that of the mainstream view. Extending this to posts on Mythology from believers, like the ones listed in the question at hand, it is important to show that you speak as all members of your group would speak. Sources can help convince everyone of that.
Mi Yodeya: What is considered a Jewish source? brought up a viewpoint I did not expect: the decision should go to the asker. As Mike wrote,
Someone who posts a question asking for "Jewish sources" might get the Shulchan Aruch, Rav Moshe Feinstein, Rashi, Rabbi Harold Kushner, Moses Mendelssohn, Martin Buber, Anita Diamant, Adam Sandler, Jon Stewart, Joe Schmo, or his brother Sholom Schlepper.
If they want to get a specific type of source, they should specify what they want. If they aren't specific, they shouldn't complain if they get stuff they are not interested in.
. . .
The above reads harsher than I might want. If it is a new user to Mi Yodeya, I hope they get a source they want, since they won't know to ask specifically. I guess throw them what answers we can or ask what kind of source they would like in comments.
This expresses a view contrary to all others: It's up to the asker. Specify the level of rigor you want and will accept. My take on this matter is that questions are for everyone, not just the person who asked them (this justifies closing questions as duplicates; if the answers were tailored to the asker, then they might not satisfy future askers/readers).
However, this is not Mi Yodeya's policy on sources; it is only - as Monica Cellio pointed out - a small part of the discussion, and I don't mean to represent it either as their policy (it isn't).
Putting all of this together, my take on the matter is that answers should provide proof that what is written therein is the mainstream interpretation of the matter at hand, that the story they give is what has been agreed upon. To do this, sources are generally needed.
But this isn't the whole story. In a comment that he since deleted2, femtoRgon wrote
I'm sensing a bit of cognitive dissonance on the negative reception of Christian testimony vs the positive reception of Sauk tribal testimony. If a testimony from the standpoint of faith is acceptable, I would call this a good answer. It's complete, direct, and provides supporting citations. The answer that prompted this question is interesting, but barely addresses the question, and provides no external sources. Hard not to see a problem there.
I don't agree with all of it, but I agree with some of it. One thing I disagree with (but was brought up in this) is that we perhaps should treat answers coming from different belief systems differently. In one of my earliest answers, I began by writing
The Aboriginal people are protective of their culture, and they do not share all of their stories with the rest of the world. For them, much of what transpired is a private matter, and so only some stories can be accessed.
All four of our indigenous-australian questions have been answered, two apiece by femtoRgon and me. I can say without doubt that I am not by any means a descendant of indigenous Australians, and while I can't speak for femtoRgon, odds are against him being one, too. All of our answers were cobbled together from various sources, many of them written by outsiders studying various cultures. I brought up pretty much the same issue in What sources should be used for answers to questions about Scientology?:
I'll quote senshin from that question:
I'd try and read up on this myself, but, you know, I'm not an Operating Thetan, so this stuff is hard to find.
Replace "Operating Thetan" with "member of culture with hard-to-find myths X" and you describe a number of situations3. What, then, do we consider accurate?
Quoting femtoRgon's answer there,
My opinion in this case (and pretty much all cases, really) is: Use the best sources you have available.
In cases where all relevant information is mostly oral history, then we should require minimal citations. This introduces loopholes, as was pointed out in this question (such as the fact that anyone could pose as a member of the Osage tribe and get away with spreading falsehoods).
Taking all of this into account, I suggest that we work off of the following policy: If there are substantial amounts of documents available (as in Christianity, for example), then we should be stringent about our requirements for sources. If there are little to no documents available, then we should require proof that the answerer is an expert in the topic at hand. As you said in this question, Christofian, we need to keep our scholarly rigor.
This has been written over the course of about ninety minutes (including time for dinner), so I apologize if some bits are a little confusing. I can clarify and edit as needs be.
1 I understand that the issues brought up in these posts differ from the one at hand. I used them to illustrate some key ideas that are relevant here. Also, I left out Biblical Hermeneutics, Hinduism, and Islam, because I could not find relevant posts there.
2 I'll remove this quote if he asks me to.
3 It is important, of course, to understand that I consider Scientology little more than a load of fetid dingo's kidneys, and not something I respect, unlike the culture of Native Americans.