It is well known and often repeated that China does not tolerate dual
citizenship, except in the case of its citizens who have right of
abode in Hong Kong or Macau.
The Chinese Nationality Law is clear about this: Article 3.
This is not true and you misunderstand what Article 3 says. Article 3 says (depending on your translation):
The People's Republic of China does not recognize dual nationality for
any Chinese national.
The only way I think this can be interpreted is that, if a person were to statutorily have both Chinese nationality and foreign nationality under each country's respective laws, then the PRC would only recognize their Chinese nationality, and not recognize their foreign nationality.
This article does NOT mean that nobody can have dual nationality under the law. In order to "recognize" or "not recognize" something, it presupposes that the thing exists. If nobody had dual nationality under the law, then this article would be meaningless, as there would be no point to "not recognize" something that nobody has anyway. This article only matters to someone who truthfully has dual nationality under PRC and foreign law.
Given someone who truthfully has dual nationality under PRC and foreign law, since dual nationality is not recognized, which nationality is recognized and which is not? Since Article 3 says "Chinese national", it implicitly recognizes the person's Chinese nationality, which means it's the foreign nationality that is not recognized. (This, by the way, is essentially identical to the US position -- the US only recognizes the US nationality of a dual national.)
It is true that true dual nationality of the PRC and a foreign country is uncommon, but that is mainly due to Articles 9 (which says a Chinese national naturalizing abroad automatically loses Chinese nationality) and 8 (which says that a foreign national who naturalizes to get Chinese nationality shall not retain foreign nationality). It is not because of Article 3.
By the way, when I say someone who has dual nationality of the PRC and a foreign country, it does not include a Chinese national who has naturalized abroad, who is subject to Article 9 but continues to use/obtain PRC passports and/or continue to exercise the rights of a Chinese citizen. De jure, this person no longer has Chinese nationality, even if the PRC government is not aware of it yet. When discovered, they will be treated as only a foreign national, and that is consistent with my explanation, since this person does not de jure have Chinese nationality. Any documents issued to them reflecting Chinese nationality after their foreign naturalization, were issued in error. Article 3 is irrelevant for such a person since there is no question of "recognizing" dual nationality for a person who does not legally have dual nationality.
So who are the people who truthfully have both PRC and foreign nationality? There are several cases.
First, as you noted, this is possible for many people in Hong Kong and Macau, due to explanations of the PRC nationality law for those territories. For example, in the one for Hong Kong, items 2-4 say that Chinese of Hong Kong are Chinese nationals despite holding foreign passports. They do not have foreign consular protection while in Hong Kong and the rest of China, (unless they choose to apply for change of nationality to foreign nationality, effectively renouncing Chinese nationality). It says their foreign passports can be used for traveling to "other countries and territories" (implying that they cannot be used to enter Hong Kong or the rest of China). This supports my explanation of Article 3 above, that the PRC only recognizes the Chinese nationality of a dual national, and does not recognize their foreign nationality.
Another case is a child born in China to one Chinese citizen parent and one foreign national parent who meets the conditions to automatically pass on foreign nationality to the child at birth according to that foreign country's law. According to Article 4, a child born in China to at least one Chinese citizen parent is automatically a Chinese citizen, without regards to whether the child also has foreign nationality at birth, or anything else.
Any person born in China whose parents are both Chinese nationals or
one of whose parents is a Chinese national shall have Chinese
And finally, we get to the case you mentioned, for children born abroad. Article 5 deals with children born abroad, and it says that a child born abroad to at least one Chinese citizen parent automatically has Chinese nationality, except when at least one parent is a Chinese citizen who has settled abroad, AND the child has foreign nationality at birth, in which case the child will not have Chinese nationality.
Any person born abroad whose parents are both Chinese nationals or one
of whose parents is a Chinese national shall have Chinese nationality.
But a person whose parents are both Chinese nationals and have both
settled abroad, or one of whose parents is a Chinese national and has
settled abroad, and who has acquired foreign nationality at birth
shall not have Chinese nationality.
Because they wrote it with an "and", it means that children who had foreign nationality at birth but where neither parent was a Chinese citizen who has settled abroad, will have Chinese nationality at birth. If they had wanted to make it so that children born abroad could not have both Chinese nationality and foreign nationality at birth, they could have written it with an "or", but they didn't.
Unlike some other countries, the PRC nationality law does not require that children born abroad be registered at a PRC consulate with a declaration that the child does not have a foreign passport in order to get Chinese citizenship. Nor does the PRC nationality law provide that dual national children lose their Chinese nationality if they don't renounce foreign nationality at a certain age.
Since you specifically ask about children born in the US, they will all have foreign nationality (US citizenship) at birth (ignoring cases of children born to diplomats). So it only depends on the other condition (whether at least one parent was a Chinese citizen who has settled abroad). The PRC government interprets "settled abroad" as having foreign permanent residency (e.g. US green card). So assuming the only relevant foreign permanent residency is the US green card, here is a table summarizing whether a child born in the US has Chinese nationality at birth, based on the status of the parents:
||Chinese citizen without green card
||Chinese citizen with green card
|Chinese citizen without green card
|Chinese citizen with green card
The current procedure at PRC consulates (both in US and in other countries) is that they issue PRC Travel Documents (旅行证) instead of PRC passports to children born abroad, who have both Chinese nationality (as determined by Article 5) and foreign nationality at birth, who wish to travel to China. These Travel Documents are passport-like booklets, are valid for 2 years (can be re-applied for again after expiration), and contain a Chinese and an English info page, both of which say, among other things,
- The bearer of this Travel Document is a citizen of the People's Republic of China. [...]
Having a US passport does not preclude the issuance of the Travel Document. In fact, the consulate expects the child in this case to have a US passport and requests the US passport information as well as the physical US passport during the application process, if the child already has one. The consulate clearly has no problem recognizing the child as a Chinese citizen even if they know that the child has US citizenship and a US passport.
This Travel Document can be used to enter and exit China. When exiting China, the child would present both the PRC Travel Document and the US passport at PRC exit controls. The border control officer will recognize, upon seeing the Travel Document, that this is the routine procedure for a dual national child, and it will not lead to problems like when both PRC and US passports are presented (even though both the PRC passport and PRC Travel Document say inside them that the bearer is a citizen of the PRC). As you can see, having a US passport is not incompatible with the PRC's recognition of the child's Chinese nationality.
If the PRC Travel Document is lost or expires while in China, the child can get a PRC Entry/Exit Permit (通行证), which again can be used with the US passport when exiting China with no problems. When back abroad, the child can again apply for a PRC Travel Document at a PRC consulate the next time they need to travel to China.
Although it is possible for the child to be added to hukou while in China, the child should not apply for a PRC passport, as it seems this will cause problems when exiting China, as you mentioned. The child should stick to Chinese Travel Documents and Entry/Exit Permits.
I have heard rumors that the consulate might no longer issue PRC Travel Documents to such a dual national child after turning 18 (perhaps forcing the child to renounce either PRC or foreign nationality), but I haven't seen any official source on this, and the PRC nationality itself does not mention any need to do anything at any particular age.
As for renouncing US citizenship, US law requires that loss of US citizenship can only occur when the person intends to relinquish US citizenship, and young children are considered to lack sufficient maturity and understanding of the meaning of renunciation of citizenship, and be too much under the influence of parents, to have the necessary voluntary intent. The Foreign Affairs Manual presumes that an age of at least 16 is generally necessary to renounce US citizenship. See 7 FAM 1292(i)(2):
Voluntariness and intent: Minors who seek to renounce citizenship
often do so at the behest of or under pressure from one or more
parent. If such pressure is so overwhelming as to negate the free
will of the minor, it cannot be said that the statutory act of
expatriation was committed voluntarily. The younger the minor is at
the time of renunciation, the more influence the parent is assumed to
have. Even in the absence of any evidence of parental inducements or
pressure, you and CA must make a judgment whether the individual minor
manifested the requisite maturity to appreciate the irrevocable nature
of expatriation. Absent that maturity, it cannot be said that the
individual acted voluntarily. Moreover, it must be determined if the
minor lacked intent, because he or she did fully understand what he or
she was doing. Children under 16 are presumed not to have the
requisite maturity and knowing intent;