I have heard that Rav Moshe Feinstein ztsl held that tzitzis should be tucked in. Can somebody give a nice summary of the reasons behind his ruling?
Rav Ahron Felder zt"l was a talmid muvhak and spent many years serving Rav Moshe Feinstein. Among the seforim he authored is the two-volume Rishumei Aaron, which contains rulings and halachic opinions from Rav Moshe that are not found anywhere else.
In Volume II O"C Siman 8 He states that Reb Moshe held there is no obligation to wear ones tzitis out so that they are constantly visible.
My father, Rav Yitzchok Frankel, Rav of Aguda of 5 Towns, and Talmud muvhak of Rav Moshe, asked rav Moshe personally about this topic in late 1963, early 1964. Rav Moshe told him to wear his tzitzis tucked IN. My father opened Mishnah Berurah 8:26 to ask why Rav Moshe argues. Rav Moshe told him the Mishnah Berurah 8:26 is commenting in response to the Mechaber (se'if 11) that "the main mitzva is ON TOP of the beged..." to which Mishnah Berurah 8:26 clarifies that it is a great disgrace to wear the beged OUT and the strings IN. We however (Rav Moshe explained) who wear the beged under our shirt, (like the mikubalim), we wear the strings in as well.
Actually, at the very end of his life Rav moshe wore his beged on top of his shirt, and the strings out, and he kept his frock unbuttoned. His family did not like it because it looked sloppy.
P.S. My father asked Rav Zaks (the Chafetz Chaim's grandson, rosh yeshiva in Y.U.) how the Chafetz Chayim wore his tzitzis. Rav Zaks said "we never knew because my grandfather NEVER unbuttoned his frock, even indoors with the family". According to the simple understanding of Mishnah Berurah 8:26 this would have been a violation of "U'reisem Oso" ... it sounds crazy to us Americans, but the Chafetz Chayim should have cut little tzitzis holes, or at least worn his frock open. According to what Rav Moshe told my father, there is no question at all.
I had discussed this once with Rav Reuven Feinstein and he had showed me the source, although my notes only say Magen Avraham 8:13. M"A mentions there that even though the talis katan is under his clothing and therefore not readily seen if torn, one does not have to remove them on Shabbos because of kavod habriyos. If the strings were to be worn out, this explanation would not work. I also recall further proof from the halacha of not wearing tzitzis out in cemeteries, but I can't recall the specifics at this time. I will try to ask again soon. Regarding the dress style, I do recall him telling me that if one was wearing a shirt untucked it would be OK to wear the strings out.
I have heard from both my grandfather and a talmid of my great grandfather Harav Chaim Ephraim Zaitchyk (a prominent rosh yeshiva in Europe and after the war an author of 33 mussar seforim), that when he was meshamesh the Chofetz Chayim, he saw that the Chofetz Chaim tucked his tzizis in. I do recall the idea that the Chofetz Chaim in Mishna Berura writes that at a cemetery regarding of whether wearing tzizis is an affront to the dead (as it mentions in the gemara in brochos not to do mitzvos in front of the dead because they no longer have the oppurtunity) that it is not because it is under his frock (or something to that idea) implying that we wear our tzizis inside our clothes. I heard from the talmid of my great grandfather, that it must be that whoever completed the Mishna Berura wrote these halachos.