I believe that, generally, who is a country's national or citizen is solely determined by the law of that country, and there is no general "international law" regarding revoking citizenship. There is that Convention on the Reduction of Statelessness, and countries that are party to it agree to not revoke citizenship if it would make the person stateless (unless the citizenship was obtained through fraud or a few other exceptions), and not let someone renounce citizenship if it would make them stateless. I don't think that the Convention says anything about the reasons citizenship can be revoked if it doesn't make one stateless. Only a minority of countries in the world are party to that Convention. For the countries you mentioned, the UK is a party to the Convention, but the US is not.
In the case of the UK, British law already largely incorporates the requirements of the Convention regarding revoking of citizenship. So if the UK follows its own law, it should not violate the Convention. Although section 40(2) of the British Nationality Act 1981 (as amended) allows the Secretary of State to deprive a British citizen of British citizenship:
(2) The Secretary of State may by order deprive a person of a
citizenship status if the Secretary of State is satisfied that
deprivation is conducive to the public good.
section 40(4) restricts it to only dual nationals:
(4) The Secretary of State may not make an order under subsection (2)
if he is satisfied that the order would make a person stateless.
(Though it should be noted that section 40(4A) provides a slightly looser restriction on deprivation of citizenship of naturalized British citizens -- their citizenship can be deprived even if it will them stateless, as long as they are able to become national of another country. I am not sure if this provision complies with the Convention. In any case, this is not relevant to Shamima Begum's case as I don't think she's a naturalized citizen.)
In Shamima Begum's case, the issue is with whether she has another nationality or not. The British government is claiming that she does, and she is claiming that she doesn't. If she really doesn't have another nationality, then she can already challenge the deprivation of her British citizenship as violating British law, and she doesn't need to invoke the Convention or international law.
The US is not a party to the Convention, but US citizenship cannot be "revoked" in the same way that British citizenship can. Loss of US citizenship is provided in 8 USC 1481(a), but only if the person commits one of several "potentially expatriating acts" "with the intention of relinquishing United States nationality", and the standard of evidence is "preponderance of evidence" according to 8 USC 1481(b). It would be necessary to prove that the person intended to relinquish US citizenship to revoke their US citizenship, and not just for "the public good" or because they committed some crime or other bad act in itself. (On the other hand, the US does allow you to voluntarily renounce US citizenship even if it would make you stateless (see 7 FAM 1215(e) and 7 FAM 1261(g)), which it wouldn't be able to allow if it were a party to the Convention.) None of this is really relevant to the case of Hoda Muthana, because in that case the US isn't claiming that she lost US citizenship at all -- but rather that she was never a US citizen in the first place because she was born to a diplomat.