Two of the writers are from Iran ... As you may know, English writing often exhibits some degrees of gender-bias, mainly the use of "he" to refer to a person with an unspecified gender.
I think this hits the nail on the head in terms of one reason why, possibly, to make the change. As comments point out (or rather, "according to the comments", as I'm not an expert in Farsi/Persian) there aren't gendered pronouns in Persian and so, to them, it presumably feels odd on a very basic level.
Is this a reasonable request?
It's presumably a piece of work that you have all put a lot of time and work into and, accordingly, have some degree of attachment to. Not to mention that it's going out into the world with your names on it. In that context, I think that any request is reasonable -- that doesn't necessarily mean that any and all changes should (or can) be made, but it's totally fair for people to ask.
They've told me this as we are close, but haven't talked to anybody else (there are 3 others).
That does, unfortunately, put you in a difficult position, as the go-between. You have my sympathy, for what it's worth.
What's the correct thing to do here? I could just ask the others, but what do I do if somebody gets offended by the request and refuses?
I would suggest that you could talk to your fellow English-as-a-first-language (I assume) co-authors about this as an abstract topic, if that would help? Ask them their feelings about it, without bringing up th specific request. I acknowledge, though, that it could, potentially, do more harm than good if it gets them set in their ways. Alternatively, explaining that it feels "odd" to your other co-authors as their first language does not use gendered pronouns might help to avoid the "political corectness" concerns that you have.
More practically, if it comes down to a (polite) debate: some people have been taught that the word "they" can not be used in the singular, but if it helps you to argue the point, Shakespeare seemed to be perfectly happy with it:
There's not a man I meet but doth salute me
As if I were their well-acquainted friend
A Comedy of Errors, Act IV, Scene 3
Now leaden slumber with life's strength doth fight;
And every one to rest themselves betake,
Save thieves, and cares, and troubled minds, that wake.
The Rape of Lucree
(Credit to Language Log)
I will confess that I am something of an evangelist for "they" as a singular pronoun, and have argued succesfully for its use in documents. I have, I think, only ever received one objection, and that was more along the lines of the change being unecessary, or a preference for using the composite (and, in my opinion, stylistically clumsy) "he or she". However, your mileage, of course, may vary.