Edit: This answer is distinctive from my other answer because this answer allows for questions in the second category if they specify up front why Jewish expertise will be necessary. The other answer does not allow for questions in the second category.
Edit: I edited categories somewhat.
The help center states that questions about "general knowledge (science, etc.) as it relates directly to Judaism" are acceptable.
I see four categories of questions that one might think are directly related to Judaism.
- Those about Judaism itself; liberally defined as Scripture, the Oral law, along with associated literature and practice. Random example: Halacha of Shechita
That is to say, questions for which these topics form the material of the question itself, rather than a mere backdrop for a question about something else (e.g. cooking, medical research, electronics, construction, etc.) in which no doubts are expressed about the aforementioned categories themselves, but rather their status is taken for granted and provides the impetus to then ask a question about something else.
- Those which are not about Judaism itself, but about other disciplines that provide information that one might want in order to facilitate his study or practice of Judaism, but whose answers are dependent on Judaism itself. It is claimed that there are questions of this category. One question which pretty much does satisfy these requirements, is: Why aren't any of the main American brands of chewing gum kosher?. (Except that it does not even facilitate his study or practice of Judaism, in the strict sense).
Those which are not about Judaism itself, but about other disciplines that provide information that one might want in order to facilitate his study or practice of Judaism, whose answers are not dependent on expertise in Judaism. Many of these could affect anybody, but happen to have some application to Jews. e.g.: Carnation Instant Breakfast substitute. E.g. What's the best way to make ashes (for weddings and/or pre-Tisha B'Av)?. The question of how to produce and transport ashes is not a question about Judaism. Nor is there reason to assume that the specified examples would have some halakhic characteristic rendering them distinct from general ash production. (We will see below that most questions supposedly in category two are actually in category three).
Questions which are not about Judaism itself, or require expertise in Judaism itself to answer, or have some application to Jews. E.g. What was the dietary source of calcium in Talmudic times?.
I would recommend limiting questions to those in the first category. However, questions of the second category would be acceptable in some cases, see below.
My problem with questions in the second category (those not about Judaism but which are predicated on Judaism) is that they are based (to a degree) on their answers, only once answered will we find out if they were somehow answerable based on Judaism. This lets in a lot of questions that ultimately are not answered based on Judaism.
For example this question whose top three answers are not related to Judaism itself, this question whose four answers make only passing reference to Judaism itself. This question whose four answers also do not any Judaism related considerations. This one which has no answers that make Judaism considerations. And lastly this one whose four answer make no use of distinct knowledge of Judaism!
Significantly, these are all the questions which have been claimed to belong to this category.
If, however, users want to ask questions in this category, that is acceptable If and only if they specify up front which sort of halakhic issues or other element of Judaism will influence the answer.
My problem with the third category (questions particularly related to Jews) is that it is quite removed from Judaism itself, and while related perhaps to Jews, remains about Jews not Judaism. The reduction ad absurdum of the category would be questions about Tay-Sachs medical research. Even though this is 100 times likelier to affect a Jew than a non-Jew, it nevertheless has 0 to do with Judaism. Indeed, any Jew could ask pretty much any question (s)he encounters while traveling through his/her religious life here. Since pretty much every element of Jewish life is religious in some sense, everything becomes on topic! To give some examples that demonstrate why this category ought not be here, consider the following example: "I want to fulfill the mitzva of saving Jews' lives. I found a person with this type of cancer. Which chemo course is better to use based on current research?" (courtesy of @doubleAA). Or similarly, I want to fulfill the mitsvah of loving my fellow as myself. My friend has an exam on pseudo-polynomial time. Can anyone direct me to resources on pseudo-polynomial time, so that I can perform the mitsvah?
The fourth category has the same shortcomings as the previous two, but it also includes random musings that a Jewish person would be more likely to have. One example of a question that would fit this is, "I was reading Harry Potter over Shabbat, and I wondered: Why didn't Voldemort begin searching for the Elder Wand much earlier on?" Another example of a question in this category is "Which regions in the world grow the most citrus fruits, such as etrogim?"