(א) יוֹם הַכִּפּוּרִים אָסוּר בַּאֲכִילָה וּבִשְׁתִיָּה וּבִרְחִיצָה וּבְסִיכָה וּבִנְעִילַת הַסַּנְדָּל וּבְתַשְׁמִישׁ הַמִּטָּה.
(1) On Yom Kippur, the day on which there is a mitzva by Torah law to afflict oneself, it is prohibited to engage in eating and in drinking, and in bathing, and in smearing oil on one’s body, and in wearing shoes, and in conjugal relations.
בְּאַנְפִּילְיָא חֲלִיצָתָהּ פְּסוּלָה כּוּ׳. לְמֵימְרָא דְּאַנְפִּילְיָא לָאו מִנְעָל הוּא?וּתְנַן נָמֵי: אֵין הַתּוֹרֵם נִכְנָס לֹא בְּפַרְגּוֹד חָפוּת וְלֹא בְּאַנְפִּילְיָא, וְאֵין צָרִיךְ לוֹמַר בְּמִנְעָל וְסַנְדָּל, לְפִי שֶׁאֵין נִכְנָסִין בְּמִנְעָל וְסַנְדָּל לָעֲזָרָה.וּרְמִינְהוּ: אֶחָד מִנְעָל וְסַנְדָּל וְאַנְפִּילְיָא, לֹא יְטַיֵּיל בָּהֶן, לֹא מִבַּיִת לְבַיִת וְלֹא מִמִּטָּה לְמִטָּה!אָמַר אַבָּיֵי: דְּאִית בֵּיהּ כְּתִיתֵי, וּמִשּׁוּם תַּעֲנוּג. אֲמַר לֵיהּ רָבָא: וּמִשּׁוּם תַּעֲנוּג בְּלֹא מִנְעָל בְּיוֹם הַכִּפּוּרִים מִי אֲסִירִי? וְהָא רַבָּה בַּר רַב הוּנָא כָּרֵיךְ סוּדָרָא אַכַּרְעֵיהּ וְנָפֵיק! אֶלָּא אָמַר רָבָא: לָא קַשְׁיָא, כָּאן בְּאַנְפִּילְיָא שֶׁל עוֹר, כָּאן בְּאַנְפִּילְיָא שֶׁל בֶּגֶד.
And in an anpeliya (felt covered shoes), her chalitza is invalid. [if a brother gets married and dies before he can have a child, the brother has an obligation to marry his widow and produce a child to be the heir of the older brother’s estate. The brother is called a yavam, the widow a yevama, and the marriage, yibum. This marriage arrangement also serves to provide for the yevama. However, if the yavam/brother decides he does not want to marry her, they perform an act called chalitza, which involves her spitting in his shoe. This is an insult to the yavam who will walk around town with a constant reminder of his failure to fulfill his obligation. An anpeliya, or slipper, as we might call them today – however - is a foot covering you wouldn’t wear around town, and thus chazal invalidate chalitza performed with an anpeliya. ]
That is to say, that an anpeliya, a slipper, is not a “shoe” – here the Gemara is explaining in its own words what you just talked about
. And we learned similarly: the donor does not enter wearing a pargod chafut and not wearing anpeliya! [this is a mishna in Shekalim about someone who goes into the Beit haMikdash’s repository of donations to count up the money, and places restrictions on how to dress.
One’s not allowed to wear a pargod chafut, something like parachute pants that has a cuff at the bottom facing inward. And anpeliya, like we said, is a slipper. ] And we don’t even need to add that he’s not allowed to wear a shoe or a sandal, because you can’t enter the main mikdash courtyard with shoes or sandals! But there is a contradiction from a brayta: That one is not allowed to wear a shoe, sandal, or even a slipper, from house to house or even within the house from bed to bed on yom kippur. Which means that sometimes people wear their slippers in their courtyards outside the house! Meaning a slipper is forbidden on yom kippur because it is potentially an outside shoe. Abaye answers: No, wearing a slipper does not provide the same aesthetic or physical benefits as a “real shoe”. Rather, the brayta forbids wearing a slipper because it’s discussing a slipper with padding, which is a joy to wear – and yom kippur is a day of not joy, affliction. Rava said back to him: And who said you couldn’t have minimal podalic pleasure on yom kippur, as long as you’re not wearing a fully protective and aesthetic shoe – as long as you’re still suffering some level of affliction. After all, raba bar rav huna – on yom kippur - would wrap a cloth around his foot before going out // to shul. Rather, rava said, there is no contradiction! The brayta that forbade wearing an anpeliya, slipper, was talking about a leather slipper: The mishna in shekalim that distinguishes between an anpeliya and a shoe is talking about a cloth slipper.
(ז) אָסוּר לִנְעל מִנְעָל וְסַנְדָּל אֲפִלּוּ בְּרַגְלוֹ אַחַת. וּמֻתָּר לָצֵאת בְּסַנְדָּל שֶׁל שַׁעַם וְשֶׁל גֶּמִי וְכַיּוֹצֵא בָּהֶן. וְכוֹרֵךְ אָדָם בֶּגֶד עַל רַגְלָיו וְיוֹצֵא בּוֹ שֶׁהֲרֵי קְשִׁי הָאָרֶץ מַגִּיעַ לְרַגְלָיו וּמַרְגִּישׁ שֶׁהוּא יָחֵף. \
And it is permitted to go out, on yom kippur, in a sandal made of bamboo or reeds. And one is permitted on yom kippur to wrap one’s foot in a cloth and head out wearing that. Because the hardness of the ground reaches one’s feet and it’s as if one is barefoot.
אבל מטייל הוא באנפליא של בגד בתוך ביתו פירש דכיון דשל בגד הוא אין כאן מנעל וסנדל כלל ואין כאן איסור יום הכפורים... ואין טעם לחלק בין אנפליא לשל שעם לשל גמי כיון דהא והא אינם של עור ... ולד"ה מותר לנעול בתי שוקים בי"ה חפי לצאת בהם לר"ה דמשום ענוי י"ה ליכא דהא קי"ל כרבנן דכל שאינו של עור או מחופה עור לאו מנעל הוא ... וכן אומ' מ"ה בשם רבותיו ז"ל כי אותם שואיקוש שעושים בקשטיליא אסור לצאת בהם למבוי שאינו מעורב כיון שאינם מחופה עור
Once it is made out of cloth, it’s not at all a shoe or a sandal, and the issur of yom kippur does not apply...And there’s no reason to differentiate between an anpeliya and something made of bamboo or reeds, because none of these are made of leather...And everyone says you’re fine wearing socks on yom kippur and even to go out in public wearing them. And the problem of insufficient innui does not present itself, for we follow the sages who say that which is not of leather or covered in leather is not a shoe...And thus said my teacher in the name of his teachers, meaning the ramban school, those shoikush things in Castille that are made of wood. It is forbidden to go out into the public thoroughfare wearing these zuecos on shabbat, since they are not covered in leather.
מתני' יוה"כ אסור באכילה ושתייה וברחיצה ובסיכה ובנעילת הסנדל ובתשמיש המיטה... ובנעילת הסנדל אם היה מנעל קרוע נר' דמותר
The Mishna teaches that on Yom Kippur, it is forbidden to eat, drink, wash bathe, anoint, wear sandals, and engage in adult activities...And when it comes to the wearing of sandals, if it were a torn sandal, it appears to be permissible.
(ח)ומותר כו'. כן למד בת"ה ממ"ש בא"ז דמותר לצאת במנעל קרוע
“And it is permitted to go out in them, etc.”
The trumat hadeshen (rabbi Israel isserlein, 14th century austria) says that rambam’s ruling - allowing wearing reed and bamboo shoes on yom kippur, is justified based on the ohr zarua’s ruling that one can go out wearing a torn leather shoe