How to book a flight if my passport doesn't state my gender?

There is not going to be a single solution here that will be applicable to all airlines everywhere in the world.

Generally, the thing to do is to contact the airline, explain the situation, and ask them what to do. I recommend that your friend gets the airline's response in writing. Then, after following their instructions, your friend can then bring that written response with them while traveling. That way, your friend will have something solid to refer to should anyone question them.

An extra tip for contacting airlines: In those cases when the airline is based in a conservative or politically religious country and might not be familiar with such topics, there is no need for your friend to mention that they are gender-neutral. Your friend may simply say (factually) that in their passport, their gender is represented as X (indeterminate/unspecified). This may maximize the chances of getting a helpful response. If the airline happens to ask why that is the case, your friend can then elaborate.

If future travel involves visiting the USA the CBP offers this:

Q: My passport shows an 'X' sex marker. How do I complete the gender portion of ESTA?

A: ESTA does not currently have a gender X to choose from on the application. It is suggested that the traveler choose whichever choice they feel most comfortable with. ESTA will not be denied solely on the gender chosen on the application.

That seems like reasonable advice for visiting any country where an X option is not explicitly provided.

You friend should be prepared use whatever gender they can demonstrate to the airline or destination country, even if it's not the gender they identify as. Realistically, this isn't a matter of their gender, it's a paperwork problem.

Meaning, if they have a valid ID, such as a Driver License or similar, with Female, then choose Female so the can comply with ID and reporting rules. This will be the case for a very long time and some countries will never offer an X option.

I can say for sure that the airlines do not care one bit about a passengers gender. The problem is they have to accurately report this data to various Government agencies.

So, it is not a matter of pick what you want. Will an Immigration or Customs officer care? Probably not, but that doesn't change the requirement to comply with the reporting standard. The point is, they will have a much easier time if the ID matches the data, regardless of the actual value.

For example, the USA's Customs and Border Protection agency requires either Male or Female on the ESTA Application and there is no way around that but matching ID is most important to them.

The reason why most passports have a gender, height, eye color, etc. stated besides a photograph is to make it easier to identify whether the person presenting the passport to the border agent is the same as the owner of the passport.

This is likely to be true for other travel documents. So, the most practical and convenient way would be to state the one you most resemble from point of view of a casual onlooker. If you look what 99.99% of the people would call a female and you had "male" written on your ticket or other documents, a border control agent might think you have stolen the ticket or documents from someone else. Otherwise, if they see that you look like what they would expect from the gender printed on your ticket, they are more likely to let you through without becoming suspicious.

Other answers already mention that the lack of gender X in the form practically means that you may choose either option and should not experience problems with this.

In addition to this I would like to add that it could be practical to choose the gender that is least likely to cause administrative issues.

Here are some cases one could think about in order of importance:

1. Do I have any document stating gender? Old passport, visa, driving licence.
2. Am I in the system? Perhaps you have flown before, then I would definitely stay consistent.
3. Do people at first sight think I would look more male or female? Of course this is subjective, but if the person would be sporting a beard it would make sense to choose M to prevent confusion at first sight.

And of course the goal should typically be for the official to 'tick the box', not to 'change the system'. So unless needed, don't give them more to think about and just show that the pasport does not contain an M or F.

When it comes to the flight itself, It won't matter much. Pick what you like, or pick what other ID you as on first sight. Airlines won't actually care.

HOWEVER

Governments, agencies, and security will care. Some countries will care a little (the USA has a binary field but won't deny based on a mismatch), other countries will care a lot (think about the countries where being trans-gender is a capital offense).

Russia is a pretty conservative country, and they generally prefer that everyone fits in their box. So if they give you two choices M or F they expect you to choose one. Now the good news is once the paperwork is over people, in general, aren't going to care there more then anywhere else, but what's important for this question is getting though security and "immigration".

So, just make sure all your paperwork matches. Make sure your flight matches your passport (it can't), your entry visa, or other travel documents, specially those generated by Russia. Essentially the goal here is to have the gender field all be the same, whether it matches your friend's gender or not.

To save your friend some trouble, if they have dominant gender features then they should choose that gender. Remember that the security guards and so on don't care; they only care about lining up discrepancies. Picking female with a full on beard is going to cause a "wait a minute" and picking male with a "full chest" is also going to cause a pause.

Again it's about making the papers match, not about the actual gender.