The proffered solution is to use singular "they" of course. Trouble is, people don't talk like that and so from a language-is-as-it-used perspective (descriptivist), always using singular "they" makes your translation worse.
I would offer a solution like this: allow the person using the translation program to specify pronoun rules.
There is a school of thought that says we should change how we use the English language. This school thinks that the proper way to speak is to assume non-binary until informed otherwise and that appealing to "what sounds right" or "the rules of grammar" is unacceptable linguistic conservativism.
I am not making that argument. I'm just raising it because it seems relevant here. I would point out that, even if you disagree with this argument, it seems reasonable to think that people should be able to choose how they use pronouns, whether their usage flies in the face of linguistic convention/rules of grammar or goes along with them.
That said, precisely because communication is a mutual endeavour, and language is a coöperative framework, there is no guarantee that -- just because you choose to use "they" in this way -- others will follow. I wouldn't be terribly surprised if, within a generation, "they" became an unmarked definite gender-neutral pronoun in English (today it is arguably unmarked in the case of an indefinite antecedent, but extremely marked otherwise). But I wouldn't be terribly surprised if it didn't, either. Language change is an emergent process and not something that can easily be forced in either conservative or radical directions.
That's subjective.
> allow the person using the translation program to specify pronoun rules
"Translation is the communication of the meaning of a source–language text by means of an equivalent target-language text" (https://en.wikipedia.org/wiki/Translation)
Allowing the end-user to customize the translation according to their own personal biases introduces an entirely different set of issues. We should no longer call it a "translation" at that point.
I don't follow. There is an argument out there that we should stop using he/she and default to they (unless informed otherwise). Am I wrong about that? I didn't say I agree with it, just that it is a proposed solution.
> Allowing the end-user to customize the translation according to their own personal biases introduces an entirely different set of issues...
Yes, and allowing people to speak introduces this exact same issue...
It's not the purpose of a translation service - to let people customize the translation such that it fits their own personal biases and sits more comfortably with their world views.
A translation service requires user input, spoken or written, which is necessarily biased based on how the user speaks/writes/thinks. The service is also biased based on the data and methods that are used to engineer it.
In my opinion, it is perfectly fine for people to be biased. Whenever I choose to write, I am expressing my personal (biased) view. But when it comes to machine translation, I think it's reasonable to object to bias and so, for contentious issues like personal pronouns, I think it makes sense to allow people to choose.
In other words: there is simply no right way to decide between defaulting to "he", "she", or "they" for third person gender neutral. I use "he" (it's how I was taught and it sounds better to me). Some people would accuse me of phallocentrism or linguistic conservatism, but fine. In modern philosophy, "she" is used. In some circles, "they" is used. I see no issue allowing the user to specify their preferred rule, though it might be technically challenging (I have no idea).
And I can guarantee you've never used this line of reasoning against translation services performing spelling or grammar checking. Yet those are also "not the purpose of a translation service".
It's always interesting to see the twists people will go to try to use post-hoc justify an opinion.