So if I'm hearing this right, if say a hand is given a masculine reference, then even if you say "her hand" it would be masculine.
i am not sure if i understand. an article is not a pronoun. a pronoun is a word that it used instead of the noun. for the noun. pro noun. you could use the noun instead, like you might hear it in japanese anime, when children or odd characters speak of themselves "in the third person".
the article is part of the bare form of the noun in gendered languages. it is inflected accordingly https://en.wikipedia.org/wiki/Inflection and stays with the word in many situations and in that bare form, article+noun, you will know the gender of that noun.
in german hand (die hand) is feminine, so i shall use foot (der fuss), which is male. the foot of a woman is always male, but you will only see the gender of the word for a body part by the inflection of the person's pronoun. in other words: you do not say "her the foot" "ihr der fuss". you inflect the pronoun. ihre hand. ihr fuss. her (female) hand, her (male) foot.
so the article of the noun foot/hand is telling the gender of the owner* and the gender of the body part. but sadly not in an unambiguous way.
* the owner being the noun - which can have a different gender than the person it is used to refer to.
regarding chosen pronouns:
i disagree that a person can or should chose pronouns. a person might "switch" genders and assume the role of the other gender and thus use that gender's pronouns.
i regard inventing or appropriating pronouns as on the same level as inventing or using a formal title. like king, lord, count, professor, doctor, sir, lady, queen, supreme ruler of the galaxy, president, village idiot. and i consider it socially unacceptable to use a title that was not given by society.
one should not get "identity" by the usage of pronouns. that is not identity. it is grammar. and grammar is supposed to convey meaning. and meaning in language is needed to be understandable by more than one person. what is the meaning of using the pronoun "it" or "they" or "xe"?
in german, selfusing "it" has no meaning, beside being an insult or telling people you have a big ego and want special treatment. even for babies you use gendered terms, once you know the name/sex of the baby. by using "it" one would not convey the meaning of not belonging to either gender. and there are only two, even in german. the third gender is lack of a gender by being unspecified, by having that gender in the bare form, or by being not applicable - which would sound like "it" would be the perfect choice, but unfortunately this is not so. the dehumanizing insult meaning of using "it" for a person is too strong a hurdle to use it. pity. would have been handy as there exists grammar for "it".
the usage of "they" in english for a single person sounds stupid and very wrong in my non native speaker ears. but the hurdle is lower, because there are some long established cases where it would be correct and of course it is not perceived as an insult. but those cases are scenarios where you typically would not even know the number of persons. it does not convey the meaning of unknown gender, it is conveying the meaning of an unknown person. using they for a known person makes no sense. also, if you use it as such, you can easily have a sentence where the reader will not know if you are talking about several persons or someone that approprated that pronoun.
i get why pronouns are important for people, but so are names and meanings of words and grammar. if it is important to someone to tell their chosen gender, they should just do so. and then use established pronouns that are fitting to their name. pronouns are supposed to be shorthand. if you overload them with gender re-affirmation, that shorthand-ness is gone and the meaning changes from simply being a substitute for a noun to a reminder of that person's chosen gender identity. (i was talking about non standard pronouns here)
i would prefer to not focus on gender/sex all the time in texts that have nothing to do with that topic. this is awful in german as well. there are people forcing the topic by using forced/constructed gender terms that are grammatically wrong and misleading. but this is the wrong way! we need to give gender less importance, not more. and citing it all the time, be it by using chosen pronouns or by using arbitrary constructed gender terms does give it a weight it should not have.
we (western free culture) live in a society where all people can do and like all things/persons. be they girly or manly, regardless of gender/sex. focussing on gender all the time is a step backward, not forward.