One of the contentions in the preferred pronouns debate comes from the United States' very liberal position on the protection of freedom of speech for an individual, which limits the ability of any government body in the United States to create a law forcing gender neutrality or any punishment for any rude turn of phrase. In fact, among legal scholars, there is some debate as to whether or not "fighting word doctrine" is still a legal reality in the United States (as the Supreme Court has yet to uphold a single first amendment case on the argument that the speech at issue is fighting words beyond the initial ruling that such an exception exists, but there are plenty of case laws that say for certain, what is not an example of fight words, and thus free speech). It's also worth pointing out that because the Supreme Court has upheld context is important and that protected speech must have some political, scientific, or artistic merit (and with a bar on artistic merit set so low, that even pornography counts as artistic enough to pass this requirement (though child pornography is one of the few exceptions and is blanket banned, no matter the context).). One particular case even held that banning of hate symbols and language is a violation of first amendment protections (the case in question overturned the conviction of a man who put a burning cross in an African American neighbor's yard. SCOTUS determined that the ban was unnecessary as there were a plethora of crimes that could have achieved a criminal charge, such as arson and intimidation or harassment charges, all of which categorize a series of behaviors that are illegal but do prohibit a statement that contains a political message.).
So politically, the push for a law is difficult. The NYC law @TOnepoet is restricted to employees of public accommodations and government employees of the City while on duty or acting as a representative of the city. Government can restrict the speech of government employees during the course of duty. One up in the air problem to arise is in artist commissions, where an artist refuses to make a commissioned work of art for someone with content that the artist does not agree with, though this is still not a resolved question (The cake baker in the most recent case before SCOTUS had his case overturned as the court had demonstrated an in appropriate bias towards him when deciding his case and the court felt that the damage was so thorough in this specific case that retrial was not feasible. The decision does not have legal weight for any other similar cases of refusal of commissioned art services.).
Those in opposition to the movement for a law will point out that it is a legal opposition only and that, when asked by an individual, they will try to respect the request. They're only request is to not be arrested for a mistake. Other opposition will respect the request if respect is earned or required in the situation. Controversial Conservative Comedian (say that five times fast... and yes, you might disagree with my use of any of those adjectives) Steven Crowder usually does not respect preferred pronouns when a person calls for a legal enforcement, to emphasize the reason why it's not feasible. However, he has had trans-individuals on his show to interview as invited guests and his (in)famous "Change my Mind" Segments when it is requested of him (in the latter case, Crowder specifically does not allow guests who will agree with him, so these guests who he uses preferred pronouns with often oppose his position on the subject.).
Most Americans do try to be mindful of the subject, but there are some quirks. As another answer proposed, English use of a neutral "He" for a generic profession holder is often used (such as a generic singular doctor may be referred to as "he" if the gender is unknown or moot, and will be corrected once the detail of specific gender is revealed). Uniquely, when refering to a generic President of the United States (even a hypothetical future one) the term "He" is almost always used unless it's specifically stated that it is a hypothetical female president. Part of this is that, at time of writing, there has never been a female President of the United States, even though the office never had a legal restriction on gender (the President did not need to meet any other historical requirement to voting (including the most restrictive requirement, owning land) so long as the office seeker met the rest of the criteria. Initially one could be a non-land owning citizen and still be president, though this did not happen. Similarly at no point was there a codified law barring women from elected office, but in practice it was not done. In fact, the language of the Constitution, except for the amended portions about voters needing to be land owning males, the use of the word "man" is in context the same as using "person" in the constitution and all legal protections afforded to citizens were not based on the gendered use of man. Given that the Constitution is seen by Americans as almost a sacred text and the ability to change it is difficult, most Americans are not particularly interested in amending instances of man used in similar contextual meaning to person, especially when the 19th amendment excised the sex based restriction on voting, the only time where one's gender was referenced in the document. That said, there is an amendment push to include this explicitly rather than rely on the jurisprudence read of the document to ensure this remains.
Gender nuatrality has largely been enforced in technical writing (such as writing user manuals and opperating orders or instructions) but because of the nature of this writing, most instructions are imperative statements, which use an implied "You" as the subject (i.e. "Go to the mall." is has an unstated second person subject so it reads "[You] Go to the mall." If the predicate noun is a singular person, pronouns are usually written as "he/she" rather then "they".
It's also important to stress that English is a gendered language but follows a very strict and very logical assignment, where only things which are capable of having gender get gendered terms while things incapable of gender do not, as well as generic members of non-human animals. In fiction, things with human personalities but no biological sex have gender that corresponds to their personality. Robots are "It" pronouns, but Lt. Commander Data is a "he" and Star Trek only refers to Data as an "it" to clue in audiences that the speaker is not a good person. This can cause some confusion when the personalities are difficult to nail down to gender (especially common in animation where a talking object has no gender role traits, given that many people lending the voice to young male characters are women). One such example is a debate among fans of "The Brave Little Toaster", a cartoon film about appliances that came to life when people weren't looking. The characters of Kirby (a vacuum), Lampy (a lamp) and and Radio (Guess) are all identified as males and have male voices. The titular appliance and Blanky (an electric blanket) are prone to fan confusion as Toaster is voiced by a woman, addressed by male pronouns in the film, but the director says he thought of Toaster as a woman, and Blankey, who's voice is unusually child-like and timid compared to the rest of the cast, but is voiced by a man, and not a woman as is typical of any child character in animation. Another bizarre character is that of Spongebob, who is typically referred to by masculine pronouns, has a romantic interest in a female character, has a mother and a father, and yet explicitly states he is asexual (that is, biologically, not that he isn't interested in sex as it usually means with humans), and once took on the motherly role in a temperary parent relationship to the male Patrick that caused some minor moral panic for possibly depicting a gay couple raising a child (though the point of the episode was more a defense of the stay at home parent, regardless of gender, and the frustration when the working parent doesn't understand that child rearing is a full time job, which is a problem any couple in such an arrangement, even one between two different species, one of whom reproduces asexually).
The reason it doesn't often come up is that English doesn't have many words that are gender dependent, lacking it's two nearest language family members gender changing articles ("The" and "a/an" are gender neutral compared to German's similar articles, which change depending on gender. The Simpsons gag of "Die Bart Die" is not proper German as Bart, a male, would be properly rendered "Der Bart Der". Die is feminin) nor do adjectives receive gender suffixes indicating nouns the adjective describes (French, and any latin based language for that matter) and in both cases, the asignment in gender is rather straight forward, where as both of the related languages are arbitrary. Gramatically, English relies on word order (like German) to which words are which, which is why German doesn't change suffixes (Generally, english and German are [subject][verb][predicate]), while Romance languages have a prefered order of words but it's not necessary (preferred is [Subject][Predicate][verb], but since the subject noun will have a different suffix then the predicate noun, and verbs conjugate differently then either of those, order doesn't matter so long as you're using the correct suffixes. "Life of Brian" mocks this (in English) when anti-Roman activist Brian grafitis a wall with an intended message of "Go Home Romans" but the exact translation uses the wrong modifiers rendering the meaning incomprehensible in both latin and the direct translation, and a confused Roman centurian catches Brian in the act and is more angry about the fact that "Romans They Go The House" doesn't say anything, then the anti-roman propaganda or the vandalism of graffiti. English does have some capacity for this as the predicate can appear anywhere in the sentance so long as the verb follows the subject. It's popularly called "Yoda speak" as the Jedi master speaks in this form exclusively. Consider the real Yoda line "My own counsel I will keep" versus a standard order of "I will keep my own counsel". Both are clearly understandable statements of the same meaning, which is different then "My own counsel will keep I" which doesn't contain valid meaning (and first person singular predicate pronoun is "me" in english). The Russian Reversal joke actually relies on the fact that "You" is appropriate in both the standard arrangement and the reversal, but it fundamentally changes the meaning of the statement (Standard: In America, you watch the TV. Yoda: In America, the TV you watch. Russian Reversal: In Soviet Russia, The TV watches you.). This is less important to the question, but fun with languages and how gendered languages use gender differently. English simplified, German keeps it for reasons only known to the Germans, and Romance Languages use it because they are very close to Latin, which used it in part to denote word order. English is mostly a Germanic langue (especially with grammar) heavy use of Romance language loan words by way of French. The simplified genders likely removed the rather confusing gender nature of German (which was functional without genders) and the difference occurred long before French entered.
Just be glad that your not Polish Royalty, where the dynastic sucession of the King of Poland was preserved when someone clever realized that the law said Poland could only be ruled by a King, not a Queen, but the law never said that the person who was King must be a male. Thus all of Poland's monarchs were Kings... especially the women who held the crown (by the way Queen denotes two different positions in English language. A female Monarch is a Queen, but so is the spouse of a Male monarch (King). The spouse is typically the "Queen Consort" to denote she is royal by marriage to the monarch, not a monarch in and of herself. The Royal female Monarch flip of this will have a Queen's spouse referred to as a Prince Consort and typically King refers to the person who may weird monarch powers, what ever they are. Polish has no word for a female monarch, so King is gender neutral title for the role, regardless of status. Similarly, the title Pharaoh didn't have a feminine counterpart so female rulers were Pharaohs. The famous false beard a female Pharaoh wears is ceremonial. Male Pharaohs without much in the way of facial hair also wore false beards. The style of the beard was apart of the traditional vestment and is much more akin to a crown in the symbolic importance.