"Well, I'm not a man, and I live here."
The above conversation is one I overheard my mother having. Being a former hippie, she's part of a movement that understood 'lady' as a trivializing term, whereas I understand it as a respectful term in most contexts.
But what does your reader understand it as? Your main character? Are they the same or different?
Worse, if you're writing for anyone under 30, what do you do for those characters for whom a gendered pronoun is not appropriate? "That person," "they," and [name] can be hard to navigate for the length of a thousand-word short story, ignoring completely the challenge of novels. First person can be a way around dealing with it in narrative, but what about how characters react to them? Does the entire cast have the same biases about a character of non-obvious gender, and if so, is that on purpose?
Even if you're keeping to gendered characters, there's the question of terminology to reference significant others; "partner" is en vogue, but with some subcultures it connotes a same-sex partner, while with others it connotes someone with whom the relationship is too serious for them to feel comfortable using "boyfriend" or "girlfriend," but which is not headed for marriage.
Gendered language is a similar minefield to that of finding politically correct skin-colour/ethnicity terms. It's worse, though, in that melanin content can be described as "Oh, you have a high melanin content." That makes for awkward phrasing, but it's possible without turning too many verbal backflips. Gendered language, though, can be broken down by people who subscribe to a gender binary, people who consider it a spectrum, and people who present socially as one thing but consider themselves another (drag queens are one example of that in play).
It's going to be impossible to please everyone. But in writing, it's a good thing to consider as part of who you're representing in your fiction and who you're speaking to.