As far as the obligation of wearing a hat during davening as brought down in the Mishna Berura, is it an inherent chiyuv or based on the minhag hamakom of how to show kavod? I saw quoted from Shu"t Tzitz Eliezer (Chelek 13 Siman 13, Chelek 14 Siman 49) that in places where people don’t wear hats to show kavod that it is possible to be lenient as long as you wear a special kippa for prayer. I didn’t see the teshuva inside, but it seems that the "special kippa" is based on the Rambam (Hilchos Tefilla Perek 5 Halacha 5, see Lechem Mishna) who uses the pasuk "Hishtachavu LaHashem B’Hadras Kodesh." If so, is even this necessary (if we don’t poskin like the Rambam here)? I also heard quoted in the name of HaGaon Rav Henach Lebowitz Shlita that it is inherent kavod to wear a hat, only that this generation lacks kavod. What is the majority opinion in halacha?

The “pshat” understanding of the halacha in the Shulchan Aruch (91,5) is that in today’s context there is no obligation to wear more than a kippa when davening. The Mishna Berura (91,12) following the Chayei Adam and in line with the “pshat” of the Shulchan Aruch, bases the obligation to wear a hat when davening on the prevailing custom whereby someone would always wear a hat when appearing before important people. Today this is of course, not the case. Among the gentiles, one doffs one hat when visiting the President, the Queen etc. and this raises another problem- if one goes hatless is he “following in the ways of the goyyim”? HaRav Ovadia Yosef (Yabiya Omer 6,Orach Chayyim 15) points out that someone wearing a kippa is certainly not following in the ways of the goyyim. Both the Tzitz Eliezer and the Yabiya Omer recommend (they do not write that this is obligatory) wearing in shul a kippa that covers most of the head (this is the special kippa to which he refers). Outside of shul, a kippa that doesn’t cover most of the head is sufficient as long as the head would be described by an observer as being covered (Iggrot Moshe Orach Chayyim I 1).