Gender is one of the first things we notice in others, as mentioned in previous posts. However, you've stated that you're thinking about writing in first person, and that the narrator is going to be part of an androgynous race. Their own gender may not be something that goes through their own mind a lot, or even at all, and if their own gender isn't something they think about, then it wouldn't necessarily be part of their narration.
Think about how a person writes a diary. You could read pages and pages of a diary without seeing a single reference to what gender its writer is, because the diary is based around the pronoun "I." Just for fun, I skimmed two weeks of Samuel Pepys at random. There is no explicit mention of the writer's gender. Sure if you know anything about London society in 1660s and make the very safe assumption that a person during that time period with a wife and these sorts of social activities is necessarily male, then you know the author's gender, but these are still assumptions. At least in the passages I read, Pepys makes no direct reference to being male. (Also, I get the feeling that concerns about referring to "my wife" revealing the speaker's gender for sure might not be as significant in a modern fantasy race.)
This can work with other character interactions, as well. When people talk to each other do they always mention the gender of the person they're greeting? They do sometimes ("Hello, Ladies"), but there are enough non-gender based options, that avoiding them doesn't really seem like avoidance. "It's been so long since I've seen you, what have you been up to?" or "Can you help me out with this life-altering dilemma?" or "Meet my new friend, Alex," or "Please put the camel in the garage," are all perfectly reasonable things to talk about with someone that don't rely on knowing the speakers' genders.
You've got the extra leverage of having an androgynous race, but I would argue that this is not even necessary. There are plenty of humans who go about their day to day business without thinking about their own gender very much - certainly not enough to write in any record of the day.
For a good example, I would recommend that you check out The Towers of Trebizond, by Rose Macauley. The narrator of this book never genders themself, and their lover is only gendered in the final pages, but a lot of people don't even mention this when they talk about this book (it's not even on the Wikipedia page), because the lack of explicitly stated gender is not intrusive; the narrator's gender is just sort of not there. This book is the best example I know of as a first person narration that never explicitly mentions the narrator's gender.
I was about 1/4 of the way through reading it before I realized that there were no gendered words used to refer to the narrator. It was the same sort of feeling as watching a movie that you didn't know was just going to be one long take with no cuts (or just hidden cuts). At first you don't even notice, then you do, and then you read/watch very closely to see what the tricks are, and then you start thinking about why this intentional lack exists, and how it impacts the overall meaning of the piece.
So doing this over the length of an entire book has the potential to send an interesting message - not necessarily that the character or the author is trying to trick the reader or hide something, but that the character's own gender just does not matter to them. It does not occur to them to have thoughts about what gender they are. The lack of character gender being mentioned in the book potentially reflects how little import the character places on their gender in a much more interesting way than them coming out and explicitly talking about it.
In summary, not only can this can be done and done well, but a carefully chosen stylistic absence can have an interesting impact on the meaning of the work that is difficult to make as impact-fully without such a constraint.