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Underneath questions on Stack Exchange sites there is a "share" link which allows one to share the question one is viewing on Facebook, Google+, or Twitter. Is it permitted to use this feature on Mi Yodeya if one has non-Jewish contacts on these sites? Does this violate the dictum of the gemara in Chagiga 13a which states "אין מוסרים דברי תורה לעובד כוכבים" ("one may not teach Torah to idolaters")?

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The Igros Moshe - יו"ד ב' סימן קלב - writes that the prohibition is only when one intends to teach Torah to non-Jews.

דהא דאין מוסרין דברי תורה לעכו"ם, הוא דוקא כשכוונתו למוסרם להעכו"ם, אבל כשכוונת הלומד דברי תורה הוא ללומדם בעצמו ולמוסרם ליהודים הנמצאים שם, לא נאסר מחמת שנמצא שם גם עכו"ם שג"כ ישמע ממילא הדברי תורה.‏

If one teaches Torah and there happen to be non-Jews within earshot one need not chase them away or stop teaching.

As long as one's intent is to teach Torah to Jews, it's irrelevant that non-Jews can also hear.

One of his proofs is from Rabban Gamliel's famous slave Tovi who was very knowledgeable in Torah, having picked it up with his master taught it. (The Rambam in Avodim 8:18 and the Shulchan Aruch in Yoreh Deah 267:71 forbid teaching a slave Torah. וְאָסוּר לְאָדָם לְלַמֵּד אֶת עַבְדּוֹ תּוֹרָה וְאִם לִמְּדוֹ לֹא יָצָא לְחֵרוּת)

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