Answer

In my personal opinion, this does not carry much force. Even in the language of the halakhic decisors, one must pay attention to whether they write it as a full obligation or as a recommendation, custom, etc. Some decisors are not careful to make these distinctions (such as the Kitzur Shulchan Aruch).
In the end, the force of all these things comes from custom, not because this or that decisor wrote it.
The same applies to the morning prayer. The custom today is to do everything.
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Questioner:
Regarding head covering and prayer, it is clear that this really is the custom. But is there a custom to put on the robe (or any garment) properly and not inside out? How do you measure whether something is indeed a custom? Likewise regarding putting on the robe (or any garment) under the blanket.
Is it correct to say that an obligation stemming from custom applies only to positive acts (a kippah, the prayer text, etc.), and not to refraining from things (not getting dressed outside the blanket, not putting clothes on inside out, etc.)?
 
Beyond that, there are customs that are practiced but are not halakhically binding—doughnuts on Hanukkah, costumes on Purim, kissing tefillin or a mezuzah, a first haircut at age three, the kapparot chicken ritual, etc. What is the criterion for distinguishing between customs that are halakhically binding and those that are not?
 
And above all, why is a custom binding at all if it is not an ancient custom but a new one? And is there not a problem here of adding to the Torah?
 
I saw several lenient sources online:
In an article based on the words of Menachem Elon:
 
I think that since most of the Jewish people do not observe Jewish law, customs no longer have the binding significance they had in earlier periods.
Many customs are today considered a halakhic obligation, and anyone who thinks the matter is forbidden, once his mistake becomes clear to him, may cancel his custom.
 
In addition, Tosafot on tractate Avodah Zarah 59a says: “If the law in your hand is uncertain, go after the custom.” This implies that where the law in your hand is not uncertain, there is no obligation to follow the custom.
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Rabbi:
1. I did not understand the question. What does it mean, how do you measure that something is a custom? If it has a source, then it is Jewish law, and if not, then at most it is a custom.
2. A custom that those who practice it themselves understand is not obligatory is a non-binding custom. That is the case with doughnuts and the like.
3. What is the difference between an ancient custom and a new custom? Every custom was once new, and after some time it becomes ancient. Customs have force, learned either from the law of a vow or from the verse “Do not forsake the teaching of your mother” (see the beginning of the chapter “A Place Where They Practiced” in tractate Pesachim). According to Maimonides, there is “adding to the Torah” only if one says about something that it is from the Torah. Not everything people practice is adding to the Torah. Therefore he writes that sages who enact or decree something must state that this is their legislation and not Torah law.
4. In my opinion, the fact that most of the nation does not observe Jewish law is meaningless. There were other periods when most of the nation worshipped idols. So what? What determines things is what those who are obligated do. In any case, a custom does not require that all of the Jewish people observe it. There are local customs, customs of particular communities, and the like.
5. Regarding a person who erred and thought it was Jewish law and it became clear to him that it is a custom, there are decisors who permit this even without annulment of vows. I am not sure about that.
6. The Tosafot you cited is an explicit Talmudic passage in the Jerusalem Talmud in several places (see Peah 7:5 and elsewhere). The meaning is that there are two kinds of custom: 1. A neutral custom (not halakhic), like doughnuts or a kippah. Its force comes from “Do not forsake,” as above. 2. A halakhic custom (the practice is to rule the law this way and not another). The second kind of custom deals with halakhic ruling, and once one rules that way it is binding because that is the law, not because of “Do not forsake.” It is just a rule in halakhic decision-making: if you do not know, go after the custom. And that is what the Jerusalem Talmud says. Therefore it is obvious that when you know what the law is, there is no reason at all to follow the custom. But that is only for type-2 custom and has nothing to do with type-1 custom. Of course, even a type-1 custom does not uproot Jewish law.
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Questioner:
1. I meant: how do you determine that something is a custom? I assume there is some blurry boundary, and let us say the custom of head covering lies deep within the territory of custom. My question is about borderline cases of all kinds of esoteric customs that quite a few people do not know at all. In other words, what is the criterion for determining whether something falls under the category of custom or not, in cases where it is not obvious?
2. Regarding understanding: it may be obvious to others which custom is binding and which is not, but to me it is not so obvious. That is why I am trying to understand how one distinguishes between the two. There are also rabbis who insist, as an obligation, on customs that other rabbis see as non-binding, and then the question arises: whom do we believe?
3. Regarding an ancient custom, there at least one might have initially thought to say that it is a custom originating at Sinai and preserving some halakhic law that was forgotten, but regarding a new custom, certainly one cannot say that.
4. The question is whether a person who is not part of any community, and whose ancestors did not bequeath him a heritage of binding customs (for example, legumes on Passover), is obligated in any customs, and if so, whose.
6. If I understood you correctly, the force of a custom such as doughnuts comes from “Do not forsake.” If so, why should it not be binding? And if it is not binding, can one infer that all the other non-halakhic customs are also not binding to the same extent?
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Rabbi:
1. Things that some people do are not a custom, except perhaps for their own community, if it is a defined community. The burden of proof is on the one claiming that something is a custom. There is no sharp criterion, and one uses common sense, as in everything.
2. See 1. The question of rabbis is no different from any halakhic question about which there is a dispute. If you are capable, you should enter into the topic and decide for yourself. If not, make for yourself a rabbi. By the way, it seems to me that usually if you ask rabbis whether, in their opinion, this is Jewish law or custom and whether it is binding, they will answer you straightforwardly.
3. A custom is not law that was lost to us. It is, by definition, an innovation. An ancient custom is not more credible in my eyes than a new custom, except that if it has spread throughout the public, then it is binding by virtue of custom. Of course, this depends on which of the two types of custom I defined in the previous email we are discussing.
4. No. Only customs of the Jewish people as a whole.
6. Because even those who practice doughnuts will tell you that it is not obligatory. I also have the practice of reading interesting books, and I assume most members of my community do too. Does that make it a custom in my community? The same applies to eating cottage cheese for breakfast.