Something that would cut down on the amount of work involved in designating gender neutral pronouns for languages that don't have them could be having three options: male pronouns, female pronouns, and custom pronouns. With custom pronouns, a person can type in any sort of pronoun they want (whether that's a common one like "they" or something more unusual) and list how they want it conjugated in different sentences. Like so:
he/she
Enter Equivalent: they
himself/herself
Enter equivalent: themself
his/her
Enter Equivalent: their
his/hers
Enter Equivalent: theirs
For languages that have more or fewer conjugations of pronouns, you could simply remove or add relevant options.
Admittedly, this wouldn't cut down on all of the grammatical issues with different languages. For languages that are more heavily gendered than English, maybe give players the option to pick which gender in that language to use while still inserting custom pronouns? It wouldn't be ideal, but it would be an improvement.
Say...
Ille (custom pronoun I came up with on the spot) est belle
or
Ille est beau
I think this would be an easier option for EA that's more likely to please everyone than just adding, say, one specific neutral pronoun. It would make it a slightly more difficult feature for players to use, since the job of considering grammar is left up to them, but as an agender person myself I wouldn't mind putting in the extra effort.