Actually, the thing that is sexist is “gender selection.” It is sexist to ask for the person’s gender at all. Why do you even need to do that? The answer to that question will be sexist by definition. You are trying to separate men from women and the result of that will almost certainly be to treat the women as second-class citizens. Even the most benign version of your sexism is going to be assuming the women want fashion tips while the men want sports scores. What you should actually do is just have one kind of person called “person” and then ask the user if they are more interested in fashion tips or sports scores or both? Ask them to choose from 10 colors for their profile page rather than assigning women pink and men blue or similar. Let people sort themselves into groupings by their own interests, rather than you making sexist assumptions. You can’t make those assumptions because we don’t have strict gender roles. Men bake and women watch football and non- gender-binary people work on cars. And you can rotate the previous sentence around like a carousel and it will always still be true. So the gender information is essentially useless.
So the fact that you started out with a sexist design decision to collect the person’s gender is what leads then to sexist stereotypical icons of a bald/bearded guy and long-haired girl, and then leads to dealing with other gender identities, and you are down a rabbit hole. What Facebook did with 52 (or whatever) gender identities was well-meaning, but what they really should have done was stop asking about gender in the initial profile step at all. Let that be something that people declare about themselves optionally as they customize their profiles. Instead of “male/female” in the initial profile creation, show a list of 10 personal preference questions that sort people into marketing group A/B/C/D/E/F based on their own preferences. That not only removes the sexism, it gives you more accuracy, and it gives you more granularity because you have 6 marketing groups instead of two. Or use any number you like.
In short, if you want to stop being sexist, don’t separate people by gender, rather let them sort themselves into non-sexist groups based on their own self-declared interests and characteristics.
I’m pretty sure that Twitter is an example of doing this right. They don’t ask your gender and they have one gender-neutral “egg” icon that represents every user until they customize it with a photo of their own choosing. Then they market to you based on your tweets. If you tweet about hockey they will market sports to you, no matter what your gender. If you tweet about lipstick they will market makeup to you, no matter what your gender. That is non-sexist.