Shiurei Torah to Nonreligious



I have the special merit of teaching Torah classes in a less religious area in Bet Shemesh. It occurred to me though, many non-religious people stated attending the lectures , but they attend without a Kippah on their head. I am not sure whether to ask them to cover their head out of respect , or since that request might turn them off from attending, maybe I should let them come even without a head covering?



Do not say anything to them. Since they are not saying Shem Hashem, nor are they repeating the lecture after you, we can be  less particular about them covering their head if it will turn them away.
The Gemara in Kiddushin (31a)  quotes Rav Huna Brei D’Rav Yehoshua who said he never walked more than 4 amot without his head covered. The commentaries argue whether this is an actual prohibition, or it is just stringency.
The Kolbo ruled that it was only a pious stringency since only Rav Huna Brei D’rav Yehoshua, who was an Amora, praised himself for that, it is only a Midat Chassidut, a piety.
Maran Beit Yosef (OH 8)explains the Tur that it is a real Halacha.
The Magen Avraham ruled that more than 4 amot without a head covering is forbidden, but less than that is only a Midat Chassidut.
That is the Halacha by walking but sitting without a Kippah is more lenient. So ruled the Ba”ch. The Ta”z(8:3) (and the Shulchan Aruch Harav)however  rule it is forbidden to sit without a head covering as well. The Mishna Berura (2)12)  adds that studying Torah without a Kippah is forbidden.
HaRav Ovadiah Yosef ruled that since in in Siman 2,the Shulchan Aruch ruled tht the rei s a obligation to cover your head however in Siman 91:3 The Shulchan seems to say that there is no prohibition of not covering one’s head except in a Bet Knesset or when he says a bracha (Shem Hashem) it seems the Shulchan Aruch held that it is only a Midat Chassidut to wear a Kippah
Therefore, since if the lecture was in a house there is enough precedent to not ask them to cover their head. If it takes place in a Bet Knesset, they must put one on
The last question is whether you must tell them to put one on?
The Shaarei Teshuva (93) quotes the Shvut Yaakov, “If a big official comes to a Bet Knesset it is permitted to take off your hat to honor him, since it is  only a Midat Chassidut to wear a Kippah in a Bet Knesset. However, if you can convince him to let you wear a Kippah it is better.”  We see there is no obligation to tell someone to put on Kippah.