Trump - The positives - (see Mod note in OP)

If there's no benefit, then why bother stating a gender on the passport in the first place? To satisfy the idle curiousity of the immigration officer?

Actually, that's a good question.

I'm sceptical that adding sex/gender to passports does very much at all to improve their utility for identification purposes, or that it ever did. When you've already got somebody's name and date of birth and a unique numeric identifiers, I struggle to think that there are going to be many cases in which there remains any ambiguity that is going to be resolved with information about gender.

My guess is that it was originally included in passports because citizenship rights varued with gender. In the past, a woman who married a US citizen thereby acquired US citizenship. Conversely, a US citizen woman who married a non-citizen lost her US citizenship. And no doubt there were other sex-linked differneces in the nature and extent of citizenship rights. And the US wouldn't have been by any means alone in this. So it made sense for citizenship records to include data about sex. (And, fun fact, the main point of a passport is not to indentify you; you can usually identify yourself. It's to provide evidence of your citizenship.)

Nowadays, gender is much less likely to be relevant for citizenship purpose, but gender still appears. I suspect this is largely a historical hangover — it has always appeared; why remove it? And this may be reinforced by international standards and conventions about passport design. (It's not a coincidence that all passports look like, well, passports, and that they are all laid out in a similar way.)

Some countries do admit a third gender marker as an alternative to 'M' and 'F' — 'X', which may indicate a non-binary identification, or it may indicate an undetermined gender or an intersex person, or it may just indicate that the passport holder chooses not to add their gender to their passport — different countries vary as to the circumstances in which they use the 'X' marker. And the fact that this is permitted, and doesn't seem to cause any problems, tends to confirm that the gender marker isn't really relevant to identification — people seem to get indentified just fine with a gender marker of indeterminate meaning.

Also worth noting that lots of countries permit the use of 'M' and 'F' by reference to transitioned gender, rather than gender at birth. And, actually, if your main concern really is with identification, this makes sense — a trans person is more likely to present with the appearance of the gender to which they have transitioned than of the gender to which they were assigned at birth, so in these cases recordiing only brth gender seems more likely to confuse the process of indentification than to simplify it.

To be fair to the administration, they do not pretend that their insistance on designating birth gender in passports has anything at all to do with identification, or for that matter with citizenship. The executive order which was challenged in the Supreme Court is very open about being motivated by ideological considerations, asserting that "efforts to eradicate the biological reality of sex fundamentally attack women by depriving them of their dignity, safety, and wellbeing", and that "the erasure of sex in language and policy has a corrosive impact not just on women but on the validity of the entire American system". There isn't a word in the order about the utility of passports for identification or, indeed, their utility for any purpose at all.

In Ireland, if you get a gender recognition certificate, you can then get both a revised birth certificate showing your preferred gender, and a passport showing your preferred gender.

(You don't have to — once you get the GRC it's up to you to use it to get a revised birth cert and/or a new passport, so in theory you could use it to get one of these but not the other. But I can't imagine that many people who are motivated to get a GRC would want to do that.)

Things are more complicated in the US where birth registration is a matter for the states, but passports are issued by the federal government. The states vary in their practice — there are some states where you can get a revised birth cert showing your preferred gender and/or which will issue birth certificates with an 'X' gender marker or something of the kind, and other states where you cannot. States that do allow revised birth certificates may differ in when they allow them. For example, in California you simply assert your preferred gender; in New York you'll need a medical affidavit; in Alabama you'll have to have undergone gender reassignment surgery; in Tennessee no change is possible under any circumstances.

The new rules US on passports apply irrespective of what your state-issued birth cert says or doesn't say.

(Even if you do have a revised birth cert the registration records held by the state do show both your original registration details and any changes, so information about your originally-assigned gender isn't irretrievably lost; it just doesn't appear on a birth certificate issued today. So if the Feds really, really want to, they can find out what gender you were registered with when you were born. In practice, I don't know whether the US passport office is going to double-check every birth certificate presented to them to see the details in the state register of births are different from what's in the certificate.)