Please note that the following answer is not a halachik ruling and should not be read as such. It is a theoretical answer that explores the issue, examining the relevant issues.
With regard to the Gemara in Shabbat 33a, it seems clear that the context of discouraging sexual discussion is only when it is done in banter and tastelessly. When it is done for the sake of Torah, it seems clear that the restriction of Nivul Peh would not apply. As such this would be no reason to prohibit discussions of this nature.
With regard to the Mishna in Chagiga, the Rambam rules in Hilchot Issurei Bi'ah 22:17:
אין דורשין בסתרי עריות בשלשה מפני שהאחד טרוד בשאלת הרב והשנים נושאין ונותנין זה עם זה ואין דעתם פנויה לשמוע שדעתו של אדם קרובה אצל עריות אם נסתפק לו דבר ששמע מורה להקל לפיכך אין דורשין אלא לשנים כדי שיהיה האחד השומע מפנה דעתו ויודע מה שישמע מן הרב.
We do not relate the hidden matters concerning forbidden sexual
conduct to three students. [The rationale is that] one will be
absorbed in questioning the teacher, the other two will be debating
the matter back and forth and will not be free to listen. Since a
person's mind is aroused by sexual matters, if a doubt arises
concerning something he heard, he may [in error] rule leniently.
Therefore, we teach only to two. In this manner, the one listening
will focus his attention and recall what he will hear from the
This halacha indicates that the reason one may not relate these hidden matters to a small crowd is because when the teacher teaches, listeners might be so involved in their own discussions that they might miss something critical and rule leniently.
Given the detail of Even Ha'ezer, Rambam Issurei Bi'ah and so many of our other critical sources, it seems that we are not worried about a student misreading something in a text written regarding the relevant laws. A forum like Mi Yodeya has the same advantage as a text, that since all the content is organized on the page, if one has a doubt, he could simply re-read more carefully.
Additionally, when the forum is abundantly clear that its mission is not to provide halachik rulings, and that none of its content should be taken as such, we should potentially not be worried that he will act without consulting a qualified rabbinic authority. (Unfortunately, one never knows who is relying on Mi Yodeya for halachik rulings, but this is a problem that applies to all halachik questions equally, even those of a non-sexual nature.)
For these two reasons it seems to me that such discussions should be permitted.
Nonetheless, in this journal article Rav Hershel Shachter quotes Rav Moshe Feinstein as to broadening the definition of Arayot to include family planning and similar matters. In doing so, he prohibits discussing these matters in journals available to the public. Nonetheless, Rav Shachter writes that many of these articles have been published nonetheless, and that he published this essay of family planning on the insistence of several gedolim.
In Igrot Moshe Even Ha'ezer 1:64, in his introduction, Rav Moshe Feinstein asserts that in this society, people are searching for any justification to be lenient in matters like family planning where people's emotions and desires overtake them. As such, he recommends viewing matters like these in the same light as forbidden sexual conduct as prohibited by the Mishna in Chagiga and in the Rambam in Issurei Bi'ah.
He asserts shock at seeing such a strict matter appear in a monthly journal. He defends the publishing of Teshuvot about such matters on the basis that only wise sages who wish to clarify the truth of the halacha read these Teshuvot. Monthly journals, and to my mind certainly web forums like Mi Yodeya, are read by average folk who do not have the necessary fear of heaven to read these publications with the necessary fear of heaven.
I have two primary objections to the line of logic taken by Rav Moshe Feinstein:
- These matters have appeared in many codes of Jewish law that have been accessible to the public for a long time, and not simply obscure Teshuvot. They have been discussed in regular halachic codes such as the Kitzur Shulchan Aruch in graphic detail.
- Neither the Rambam nor Shulchan Aruch describe written accounts of
Arayot to be prohibited. One has to ask why this is, if not for the fact that they are not worried about the mishna in Chagiga unless the discussion is a face to face discussion.
It is also important to note that despite acknowledging and sympathizing with Rav Moshe Feinstein's position, Rav Shachter did in fact write a journal article intended for the public forum.
Nonetheless, in deference to Rav Shachter and Rav Moshe Feinstein, I cannot at this point encourage discussing Torah of this sort on websites like Mi Yodeya which are accessible to the public at large.