Generally in modern writing, Gender Neutral They/Them pronouns are only used when speaking of a generic person (i.e. "If someone wants to be President of the United States, they must be 35 years old." Despite the position having only ever been filled by men, it has never been blocked by an individuals gender by law.) or the specific individual is identifies as Non-Binary.
That said, I have one character who I never settled on his sexuality other than on any form that asks for his name and sex, he would answer the later question with "Yes, Please!" (he's a male horn dog... and that's not the best way, but he has frequent dates that do not result in a committed relationship) nor is it important to the plot of the story (He's a major support character.). For this reason, when the subject of his love life comes up, the most consistent feature mentioned about his partners is they all have unisex names or are referred to diminutive names that are gender neutral and the conversations avoid using the partner's pronouns (For example, he would talk about his date with Alex, but nothing about Alex can with any certainty nail down if the partner is Alexander or Alexandra.). In all cases, the main character and the secondary character have settled on a platonic relationship only long before the story started (If the secondary character has a sexual preference for the main character's gender, the secondary character has come to respect that any attraction will not be reciprocated OR the friendship is old enough that it pre-dates puberty and they were platonic best buds OR he also has a type and the main character is not that type.).
And to give you an idea of how easy it is, reread the above paragraph and notice how I use He/Him for the secondary character, but the main character is never referred to by any pronoun.
If hiding the character's gender is important to the plot, I also take steps to avoid using the character's pronouns be referring to them by features of their visual appearance and describing them in clothing that does not betray gender (I.E. the hooded figure's body was covered in by a cloak that hid it's body and making it difficult to discern the nature of the creature's physical strength.) or by using a first person perspective for the character I'm concealing (The narrator would refer to the concealed character with gender neutral I/Me while most conversations directed at the narrator would use a second person you/you.).
Additional concealing terms, like a professional title that is gender neutral but the mind may think to a particular gender. Consider the following brain teaser:
A man and his son are in a car crash and are unconscious and rushed to the nearest hospital. The boy is the first to arrive and the EMS summons over the first doctor he sees. The trauma surgeon on duty takes one look at the boy and says "I cannot operate on him, he is my son!" How is this possible.
The "correct answer" relies on the fact that at no point is the doctor's gender mentioned and it turns out that the doctor is the boy's mother and the teaser was written for an audience that would assume the doctor was a man (it told well before gay marriage allowed for the doctor to be the boy's father and the injured father's husband or for a situation where the boy's biological mother divorced his biological father and remarried the step-father who the boy regards as a father).
Since most professions in English are gender neutral and many people are familiar with a gender neutral "He" (never a hard rule, but back when non-binary gender identities were not accepted or acknowledged, the third person masculine pronouns were used for a generic person of no identified gender (it is considered extremely rude to refer to a person as "it" even if you do not know their gender as it implies a lack of personhood.), not to mention that most jobs had glass ceilings that prevented woman from perusing them, many people to this day will identify people of a traditionally male dominated profession as male when left to assumption. The only professions that avoid this are teachers, flight attendants, those who act for a living, and royalty. The former two are because the field has largely been dominated by women while the later two stem from having two words that specifically denote the gender (actor/actress with actor becoming more gender neutral in recent usage) or more (In English, the word Queen denotes both a Queen Regent (A woman who inherits the the throne) and a Queen Consort (a woman who marries the King) while King only denotes the male equivalent of a Queen Regent. A man who marries a Queen Regent is a Prince Consort or Prince).
Speaking of Royalty, the distinction of King/Queen and Prince Consort is an Englisht thing. There are some cultures where the equivalent word for King is gender netural while the Consort title is gender specific. For example, the Egyption title "Pharaoh" is gender neutral and specifically refers to the person who is the Regent regardless of Gender (though several females who held the title of Pharaoh were depicted with more masculine features and several wore false beards when making official appearances, but clean shaven male Pharaohs wore false beards as well). Similarly, the Polish Language has no word for a female regent and the title that translates to "King" is used regardless of the gender of the regent because the word for "Queen" exclusively refers to a Queen Consort and not a regent, most famously one of Poland's best known rulers, King Jadwig, was the first woman to rule Poland. So in a high fantasy setting, one could conceal the gender of a King and upon revealing the King is a woman, have an explanation that in their language, "King" is the proper title for the ruler, regardless of the gender of the ruler and have her and her court be genuinely insulted if someone refers to her as a Queen.
It's at this point, that I should point out that this is English specific and does not translate well to other languages. For example, concealing a gender in a Romantic language is harder, because gender is used to connect nouns and adjectives (and similar to English, using the neutral gender for what is clearly a human being is insulting). There are many people in Latin America who are actually insulted when an English speaker refers to a generic group of people of Latin American heritiage as "Latinex" to avoid "Latino/Latina" (I don't speak any of the languages used in Latin America, but I believe within Latin American Spanish, a generic group of more than one person of Latin American heritage would be referred to as "Latinos" or whatever the correct plural of the Masculine is. Again though, my grasp of Spainish doesn't stray far from knowing how to say "no" in Spanish). In German, women of a given profession are referred to by a feminized form of the profession (i.e. a woman MD would be a Doktorin while men are Doktors (pardon my spelling)) and will have a the feminine suffix parenthetically noted if referring to a generic member of a profession (a "Help Wanted" ad for a doctor by law must use "Doktor(-in)" in order for the employer to avoid accusations of gender discrimination). I'm not sure if a Doktorin changes the gramatical gender or not (German grammatic gender is arbitrarily assigned, and really only changes the definitive articles. Yes, the classic Simpson joke of Sideshow Bob's tattoo "Die Bart, Die" being German for "The Bart, The" is technically true, but "die" (pronounced "dee") is the "feminine the" so if the tattoo was truly German for "the Bart, the" it would be "Der Bart, Der"... of course, the phrase "The Bart, The" makes as about as much sense in German as it does in German since a proper name is not proceeded by "The" in either... but in the famous words of another Simpson's character with a grasp on the German Language, "That's the Joke".).
All in all, this isn't something for you to worry about as it is for the people who are translating your story into a language where the problem will occur.
